Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The formation and reactivity of positive Muon molecular ions Arseneau, Donald Joseph 1992

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1992_fall_arseneau_donald_joseph.pdf [ 3.84MB ]
Metadata
JSON: 831-1.0060595.json
JSON-LD: 831-1.0060595-ld.json
RDF/XML (Pretty): 831-1.0060595-rdf.xml
RDF/JSON: 831-1.0060595-rdf.json
Turtle: 831-1.0060595-turtle.txt
N-Triples: 831-1.0060595-rdf-ntriples.txt
Original Record: 831-1.0060595-source.json
Full Text
831-1.0060595-fulltext.txt
Citation
831-1.0060595.ris

Full Text

THE FORMATION AND REACTIVITY OF POSITIVE MUONMOLECULAR IONSByDONALD JOSEPH ARSENEAUB. Sc. (Chemistry) St. Francis Xavier UniversityM. Sc. (Chemistry) University of British ColumbiaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESCHEMISTRYWe accept this thesis as conformingto the required standardTIlE UNIVERSITY OF BRITISH COLUMBIASeptember 1992© Donald Joseph Arseneau, 1992IEl National Libraryof CanadaAcquisitions andBibliographic Services Branch395 Wellington StreetOttawa, OntarioK1A 0N4Bibliothèque nationaledu CanadaDirection des acquisitions etdes services bibliographiques395, rue WellingtonOttawa (Ontario)K1A 0N4Your file Votre réffirenceOur file NoIre référenceThe author has granted anirrevocable non-exclusive licenceallowing the National Library ofCanada to reproduce, loan,distribute or sell copies ofhis/her thesis by any means andin any form or format, makingthis thesis available to interestedpersons.The author retains ownership ofthe copyright in his/her thesis.Neither the thesis nor substantialextracts from it may be printed orotherwise reproduced withouthis/her permission.L’auteur a accordé une licenceirrevocable et non exclusivepermettant a Ia Bibliothèquenationale du Canada dereproduire, prêter, distribuer ouvendre des copies de sa thesede quelque manière et sousquelque forme que ce soit pourmettre des exemplaires de cettethese a Ia disposition despersonnes intéressées.L’auteur conserve Ia propriété dudroit d’auteur qui protege sathese. Ni Ia these ni des extraitssubstantiels de celle-ci nedoivent être imprimés ouautrement reproduits sans sonautorisation.CanadaISBN 0—315—79768--iIn presenting this thesis in partial fulfilment of the requirements for an advanced degreeat the University of British Columbia, I agree that the Library shall make it freelyavailable for reference and study. I further agree that permission for extensive copyingof this thesis for scholarly purposes may be granted by the head of my department orby his or her representatives. It is understood that copying or publication of this thesisfor financial gain shall not be allowed without my written permission.Department of ChemistryThe University of British Columbia6224 Agricultural RoadVancouver, CanadaV6T 1W5Date:AbstractThermal (117—445 K) ion—molecule reaction rates are measured, using the SRtechnique, for the muonated molecular ions HeMu+, NeMu+, ArMu+, andN2Mu+ reacting with a wide variety of polar and non-polar neutral species. Muis a light (0.11 amu) isotope of H with a positive muon replacing the proton. Inalmost all cases, both charge- and muon-transfer reactions are observed. Sincecharge transfer is endothermic in many cases, the reaction is believed to occurfrom rovibrationally excited states, (HeMuj* and (NeMu+)*, in accordancewith the low efficiencies of He and Ne moderators for collisional deactivation.The total experimental rate constants are generally in good agreement withcapture theories (Langevin, ADO, AADO) and in excellent agreement with thefew corresponding protonated ion measurements, regardless of the degree ofinternal excitation.The reacting muonated ions are found to form by association of a jf withthe bath gas at muon kinetic energies 1 eV, and much of the binding energyis retained as rovibrational excitation. Collisional deactivation was investigatedby varying the bath gas pressure (500’-’3000 torr) and by adding 0—2 torr Ar.A mechanism of de-excitation of (NeMuX+)* (for reactive gas X) is suggested,while direct quenching of (NeMuj* and (HeMuj* is less important, thoughit does occur.111.11.21.31.41.51.61.7Table of ContentsPositive Muons as ProtonsThe Study of Ion—Molecule ReactionsProtonated and Muonated GasesMuon BeamsMuons in GasesMuon Spin RotationRelaxation Functions14510151821262 EXPERIMENTAL TECHNIQUES 3030343711138AbstractTable of ContentsList of Tables .List of Figures .AcknowledgementINTRODUCTION.11111viviiixii2.1 Apparatus2.2 Data Acquisition . .2.3 Data Analysis2.4 Reagent Gases3 THEORIES OF ION-MOLECULECAPTURE REACTIONS 404 RESULTS AND KINETIC MODELS.4.14.24.34.44.54.64.84.94.10Identification of the Reacting TonsComparison With TheoryUnreactive Neutralsiv4143455154566365667278858891919294991013.13.23.33.43.53.6Langevin Reaction RatesThe Locked DipoleThe Average Dipole Orientation Treatments .Transition State TheoryTrajectory CalculationsQuantum Mechanical TheoriesMeasured Relaxations and AmplitudesRelaxation MechanismA Simplistic ModelA Successful Simple ModelA Mechanism with Capture and Breakup . .Complete Solution of the Capture Mechanism4.7 Other Possible MechanismsMultiple excited statesAlternative reactions and fragmentationPressure DependencesSlow Relaxation RatesTotal Diamagnetic Amplitudes5 KINETICS DISCUSSION5.15.25.31091101111215.4 Ternary Mixtures: Monitor Gas Measurements 1255.5 Comparison with Protonated Inert Gas Results 1315.6 Unreactive Ions 1375.7 Temperature Dependences 1396 EXCITATION AND QUENCHING 1486.1 Molecular Ion Formation and Excitation State 1496.2 The Reactivity of Krypton with NeMu 1506.3 Analysis of Quenching by the Moderator 1546.4 Neon Moderator Pressure and the Xe + NeMu+ Reaction 1606.5 Modeling the Anomalous Xenon Results 1636.6 Weak Quenching of the Capture Complex 1727 SUMMARY AND CONCLUDING REMARKS 177Reaction RatesIon Formation, Excitation, and QuenchingProspectsReferences 1837.17.27.3178180181AppendicesA INTEGRATION OF THE NUMBER OFTRANSITION STATES 197B TABULATED RESULTS 200VList of TablesINTRODUCTION1.1 Some Properties of the Positive Muon and Muonium,Compared With Protons and Hydrogen 61.2 Rovibrational Energy Levels and Predissociation Lifetimesof HeMu and NeMu 131.3 Binding Energies and Zero-Point EnergyShifts for Muonated Ions 144 RESULTS AND KINETIC MODELS4.1 Experimental Rate Constants Determined by Fitting )f 704.2 Dissociative Charge-Transfer Reaction Endothermicities 754.3 Results of Linear Fits ofRelative Amplitudes: A/Af vs. 1/[X] 804.4 Experimental Muon Transfer and Charge Transfer RateConstants with Total (Capture) Rate Constants 834.5 Muon-Transfer and Fragmentation Reactionsand Their Energetics 934.6 Results from Varying the Pressure at Fixed [X} 964.7 Rate Constants for the Slow Relaxation in Heand Ne Moderators 1004.8 Fits of Total Diamagnetic Amplitudes atVariable Reactant Concentrations 104vi5 KINETICS DISCUSSION5.1 Experimental Rate Constants for Non-PolarNeutrals Reacting with HeMu and NeMuCompared with Langevin Capture Rates .. 1135.2 Parameters for Dipole Capture Calculations 1145.3 Comparison of Experimental Rate Constants withVarious Capture Theory Predictions 1155.4 Results for Ternary Mixtures Employing aReactive Monitor Gas 1295.5 Comparison of Present Results with Those forProtonated and Deuterated Inert Gases 1325.6 Fits to Temperature Dependences Compared with Theory 1416 EXCITATION AND QUENCHING6.1 Results from Measurements of ArgonQuenching of (NeMuj* 1576.2 Results of Fits to the Xe + NeMu Pressure Dependences 162B TABULATED RESULTSB.1 Tabulated Results 201vuList of Figures1 INTRODUCTION1.1 Potential energy curves for NeMu and Ne Mu with thevibrational energy levels for NeMu+1.2 The M15 beamline at TRIUMF .1.3 pSR histogram for 800 torr neon1.4 The corresponding asymmetry plot1.5 The asymmetry signal, A(t) vs. t, for 1 atm nitrogen1.6 The relaxing asymmetry signal seen in neon with6.74 x i0’’ molec cm3 of added nitric oxide1.7 Two-component relaxation seen in 800 torr neon with22.5 x iO’4 moleccm3of added CF42 EXPERIMENTAL TECHNIQUES3 THEORIES OF ION-MOLECULECAPTURE REACTIONS111723232528283.1 Dependence of the Langevin distance of closestapproach r0 upon the impact parameter b 423.2 A plot of the ADO theory locking constant Cvs. /L// at 300 K 473.3 Plot of k/kL vs. = for variousclassical theories of ion—molecule capture 50viii2.12.22.3The iSR gas chemistry apparatus 31Diagram of the variable-temperature target vessel 33Logic diagram for tSR data acquisition 353.4 Comparison of the SACM, parameterized PRS, and ACCSAquantum mechanical treatments of H + HCN association atlow temperatures, along with classicaltrajectory, ADO, and AADO calculations 614 RESULTS AND KINETIC MODELS4.1 The 300 G ILSR signal A(t) for 2280 torr helium showing alarge, long-lived diamagnetic signal,attributed to the molecular ion HeMu 644.2 The relaxing signal seen in 2280 torr He with6.8 x 1014 molec cm3 of added NH3 644.3 Linear fits of vs. concentration for a numberof reactants in neon 684.4 Reaction rates of HeMu+ with various neutrals,plotted with linear fits 684.5 The SR signal A(t) showing the reaction between HeMu and2.3 x 1014 molec cm3 of nitromethane 734.6 The strongly relaxing signal seen for HeMu with35.5 x i0” moleccm3of nitric oxide 734.7 Four plots showing the variation of relative amplitudes withreactant concentration and moderator pressure 774.8 Relaxation shape for a capture mechanism witha long-lived complex 894.9 Neon pressure dependence of the fast relaxation ratefor three concentrations of xenon 974.10 The variation of diamagnetic amplitude AD = Af + A withreactant gas concentration [XJ in neon moderator, due to Muformation by the various reactants 102ix5 KINETICS DISCUSSION5.1 Plot of experimental results, expressed as k/kL vs.1/\/T = 1LD/v’2okT, for HeMu and NeMu reacting withvarious dipoles at various temperatures,superimposed on theoretical curves for varioustheories of ion—molecule capture 1175.2 Relaxation rates and relative amplitudes for the reactionof C2H6 with HeMu+ in the presenceof 5.08 x i011 moleccm3of NH3 1275.3 Relaxation rates and relative amplitudes forthe reaction of 1120 + NeMu, with6.12 x iO’4 moleccm3of added NH3 monitor gas 1285.4 The relaxation (reaction) rates for NH3 + NeMu vs. NH3concentration at 445 K and 179 K 1395.5 The experimental rate constants for NH3 + NeMu+ over thetemperature range 179—445 K, plotted as 1/v”i 1425.6 kexp for CH3NO2+ NeMu vs. 1/v’ for T inthe range 223—406 K 1425.7 kexp at various temperatures for the reaction CH3F + NeMu+. . . . 1435.8 kexp vs. 1/’, as above, but for the HeMu ion 1435.9 The two values of kexp at different temperatures for theCH3HO + HeMu reaction, compared with capture theory . . . . 1445.10 As above, for C2H4F over the temperature range 148—406 K. . . . 1445.11 Results for N20 + NeMu+ at various temperatures 1455.12 Experimental rate constants for Xe + NeMu+ over thetemperature range 117—445K, plotted as 1/v’ 145x6 EXCITATION AND QUENCHING6.1 The effect of argon on the total reaction rate of NeMu+with N20 and NO monitor gases 1566.2 The effect of argon quenching on the amplitudes for N20 andNO showing how the endothermic N20 reaction is affectedmuch more by quenching than the exothermic NO reaction 1566.3 Simultaneous fits of equation (4.29) to the neon pressuredependence of the fast relaxation ratefor three concentrations of xenon 1616.4 The simple model fitted to a representative syntheticdata run based on the Xe model 1666.5 The near-linear dependence of Ac on idealized reactantconcentration for a series of synthetic runs showing an apparentk = 3.7 x 10_b cm3molec’ s1 although the value used togenerate the data was k = 11.0 x 10_b cm3molec’s’ 1686.6 Experimental results for Xe + NeMu at 177 K 1696.7 Results synthesized to mimic the Xedata shown in the previous figure 170xiAcknowledgementI wish to express my appreciation and gratitude to the numerous people I haveworked with during my tenure as a graduate student. Drs. David Garner, MasaSenba, and Ivan Reid have made major contributions both to the research forthis thesis and to my education. Thanks are also due to my colleagues JamesKempton, Alicia Gonzalez, Randy Mikula, Susan Baer, James Pan, Alexandra Tempelmann, and Rodney Snooks; our research and discussions have beenhelpful, stimulating, and fun.It is my pleasure to acknowledge the help and support rendered by Dr. Donald Fleming, who has shown not only enduring patience in his role as supervisor,but enthusiasm as a research colleague. Thank you.Finally, I wish to thank my parents, Donald and Grace, whose teaching,love, and support have brought me this far.xiiChapter 1INTRODUCTIONThe study of gas phase ion chemistry has a long history dating from the beginning ofthe 20th century when it was spurred by the development of mass spectrometry andthe attendant need to interpret extraneous peaks. The first molecular ion identified wasH [1] whose formation was correctly attributed [2] to the ion—molecule reaction(1.1)and HeH+ was discovered not much later [3]. Protoriated ions have been well studied eversince. Interest waned somewhat in the 1930’s due to the improved vacuum techniques ofthe time, but enjoyed a resurgence in the 1950’s after the Manhattan project had pushedion beam development and CH had been unexpectedly discovered [4]. Since the 1970’sthere has been a continuing explosion in the study of ion—molecule reactions, and althoughrecent interest has expanded towards negative ions and ion clusters [5], protonated ionsare still central to the field of molecular ion chemistry. Though their importance to theunderstanding of mass spectrometry has long since passed, ionic reactions still have important applications in the fields of plasma physics, especially for relatively cool plasmas,radiolysis, astro-chemistry [6—9], and atmospheric chemistry [10], both for the earth’supper atmosphere and for other planets.12Ionic reactions are very important for building molecules in interstellar clouds [6—9],especially in dust-free gas clouds (since neutral reactions proceed mainly on the surfaceof dust grains [6,7,11]), and many extraterrestrial ions have been identified spectroscopically [6,7]. Ions are produced by photoionization by stellar UV radiation or, in darkregions, by cosmic rays. The H ion has been sought spectroscopically in interstellarspace, and while H2D+ has been detected [12], H has only been seen in auroral emissionson Jupiter [13,14]. Nevertheless, H is regarded as an important interstellar reactant [15],as are a number of other protonated species, especially HCO+ [9,16].Another significant astrochernical ion is protonated helium, though its role is not pivotal. Despite helium’s natural abundance, and notwithstanding a premature report [17],HeH+ has yet to be discovered outside the laboratory [18], though its presence has beenimplicated in the tenuous interstellar medium [19], in planetary nebulae, and in otherirradiated dense clouds, including the ejecta from supernova 1987A [15,20]. Helium isionized by UV or cosmic rays, and, in dense clouds, usually reacts by charge transferwith heavier atoms/molecules to form N+, 0+, and particularly C, which react furtherto form still larger ions and molecules. In low density clouds or in the vacuous interstellarmedium He will radiatively associate with H to form HeH [21]. Alternatively, HeHmay be formed byHe + H2 —f HeH + H (1.2)or by excited’ dihydrogen ions(H)* + He —* HeH + H (1.3)although neither of these reactions is favored. In each case, the HeH+ formed is a precursorto the formation of heavier, more stable ions.1 Throughout this thesis, an asterisk is used to indicate excited species, whether thatexcitation is electronic or vibrational.3The protonated rare gases are interesting for other reasons too. They are the simplest closed-shell molecular ions (with HeH+ second only to the open-shelled H for fewestparticles) and so are probably the best examples of point-charge molecular ions. Theyare extremely strong acids, even in the Brønsted—Lowry sense of a proton donor; forinstance, based on the proton affinities of 371 and 1400 kJ/mol for Ar and Cr, respectively, ArH is a much stronger gas phase acid than the isoelectronic IIC1, with NeHand HeH+ stronger still. Measurements of proton transfer are important for setting suchacidity scales [22—24], and comparisons of gas phase acidities with liquid values can provide valuable information on solvation, and how it relates to molecular/ionic structure.HeH+, NeH+, and ArH+ are isoelectronic with H2, HF, and HC1 respectively, and theyare the ‘nuclei’ of the Rydberg atoms HeH*, NeH*, and ArH*. It is a bit strange, then,that reactions of the protonated rare gases have received only limited study. There areextensive measurements of proton transfer from other protonated gases [24—26], but withrelatively little data on the protonated rare gases, and in particular, there are practicallyno measurements of NeH+ reactivity [26].This thesis is concerned with the formation and reactions of the muonated inertgases: HeMu+, NeMu+, and to some extent ArMu+ and N2Mu+, which are isotopomersof the protonated gases with the proton (Hj replaced by a positive muon (i = Muj.These ions react with a wide range of neutral atoms and molecules by a combination ofmuon transfer (in analogy with proton transfer) and charge transfer (forming Mu =analogous to H). Only a few of the corresponding H-ion reactions have been studied before. The results to be presented herein, along with the portions already published [27,28],extend the data base considerably, particularly in the area of charge-transfer reactions,which are rarely observed for protonated gases. Furthermore, the pressure range investigated ( 1 atm) is far above what is accessible to other experimental methods, and acomparison could reveal whether some H-ion rate constants, especially for slow reactions,are truly bimolecular or are instead due to termolecular processes.4The very low mass, only 1/9 the proton mass, raises the possibility of entirely newbehaviour. Quantum tunnelling could greatly increase the reaction rate, especially formuon transfer, in the same way that it enhances neutral Mu reactivity [29—31]. Tunnellingof hydrogen (H and H2) through the rotational barrier has been seen in the break-up ofion—molecule complexes [32—35] but tunnelling is not generally as important for ionicreactivity as for neutral chemistry. The light also gives muon molecular ions muchhigher vibrational zero-point energies and more widely spaced rotational/vibrational levels than their protonic analogs. These should affect the energetics of reactions, especiallyin regards to vibrational excitation and quenching. Some studies [36,37] of deuteratedand protonated ions have attributed isotope effects to the differences in the densities ofrovibrational states; such effects should be much larger for muonated ions.In addition to comparisons with protonated ions, measurements of muonated gasesshould prove useful for interpreting ILSR results in liquids and even in some insulatingsolids. Much of the diamagnetic tSR signal in liquids and even very-high-density gasescan be attributed to molecular ion formation [38,39]; N2Mu+, COMu+, and O2Mu+ havebeen clearly implicated in iSR studies of condensed N2, CO, and 02 [40—42], as hasH2M11+ in similar studies of solid H2 [43]. Studies of muonated molecular ions in the gasphase should increase our understanding of those environments. The present study hadits origins in an earlier investigation of gas-phase Mu formation [44], which identified thediamagnetic species in noble gases as molecular ions, and which even detected somerelaxation in Xe/Ne mixtures, though the form of the relaxation was not then resolved.1.1 Positive Muons as ProtonsMuons are elementary particles which were first discovered in cosmic rays [45] but arenow produced artificially with particle accelerators. They come in two charge states,it and . To a particle physicist, a muon resembles an electron as they both belongto the class of particles known as leptons, but a muon is heavier, weighing 207 times as5much, and unlike the electron (or positron) a muon is unstable, decaying weakly with amean life of 2.2 gus. To a chemist though, a positive muon is more like a light proton witha mass of 0.11 amu.Although muons do not feel the strong force and do not form nuclear matter as protons and neutrons do, a positive muon does form an atomic bound state with an electronjust as a proton does in hydrogen. This is the muonium atom (Mu = +e_). Since amuon is much heavier than an electron, it remains an almost stationary nucleus, givingmuonium a reduced mass 0.996 as great as hydrogen’s. Consequently, their Bohr radii,ionization potentials, and other properties are nearly identical, as shown in table 1.1.Unlike the positronium atom, muonium can truly be regarded as an isotope of hydrogen.But what an isotope! Muonium is only 1/9 as massive as hydrogen or 1/27 as heavyas tritium! This great difference is commonly exploited by jiSR to investigate the massdependence of H atom reactions and other physical processes involving hydrogen. Ofparticular import for this thesis is the ability of a positive muon to attach to a neutralatom or molecule to form a muonated molecular ion analogous to a protonated ion, andthe subsequent reactions such ions undergo.1.2 The Study of Ion—Molecule ReactionsIon—molecule reactions are studied by a wide range of techniques which fall into twobroad categories: ion beams/traps and flow/drift tubes. These have been thoroughlyreviewed elsewhere [46—51] but brief synopses of the methods are given below to highlightthe differences with the techniques used for this thesis.The original means of examining ion—molecule reactions was to use a mass spectrometer with a less-than-perfect vacuum. The straightforward extension of this is thehigh-pressure mass spectrometer, where the ionization region may be at relatively highpressure (— 5 microtorr to 1 torr), but with the mass selector and detector at low pressure.The reactants are mixed together in the ionization cell, allowed to ionize and react, and6Table 1.1 Some Properties of the Positive Muon and Muonium, Compared With Protons and Hydrogenvalue () ± value (p+) ÷ value (e)Charge +1Spin 1/2Mass 105.6595MeVc2 0.112610 206.7687Magnetic moment 4.4905 x 1023erg0 3.18333 0.004836Mean lifetime 2.19713 sGyromagnetic ratio 13.5544kHz0 3.18333 0.004836value(Mu) ±value(H)Mass 0.113978amu 0.113093Reduced mass 0.995187 me 0.995729Ionization potential 13.533 eV 0.9952Bohr radius 0.5315 A 1.0044Hyperfine frequency 4.4633 GHz 3.14237products diffuse to the mass spectrometer orifice where they are sampled continuously.Although it is easy to monitor a particular reactant or product, it is difficult to characterize the reacting mixture. Ionization is typically achieved by electron impact (from afilament) on the appropriate gas or on an inert gas (helium) which may transfer chargeto another molecular gas mixed with it. By using low energy electrons, excited helium(metastables) can be produced which create the desired ions through Penning ionization. Most of the instruments mentioned below have similar ionization regions and massspectrometric ion detectors, but different ways of selecting the reactants.Given a suitable ion source, the ions may be selected, accelerated by an electric fieldto a particular energy, and the resulting beam collided with another ion beam or a molecular beam. Toll beams [51,52] allow the most detailed study of reaction dynamics, in principle selecting reactants according to mass, energy, and internal state, while identifyingall products, their energies, internal states, and trajectories. Measured differential crosssections may be integrated to give total cross sections, which give rate constants uponfurther integration over an appropriate thermal energy distribution (the beam energy isnon-thermal). In practice, not all these goals are attainable, with limitations on signalintensity (seeing any reaction at all!), on minimum feasible beam energy (which preventsmeasurements at energies appropriate to low temperatures), and on characterization ofreactant and product states.A more generally practical technique is to trap the ions while they react, and thepreeminent trap is the ion cyclotron resonance (ICR) cell [47,48,53]. In this device, ionsproduced by electron impact are constrained to circle or spiral in an applied magneticfield, and they are detected by applying RF at the cyclotron frequency and either measuring the small RF power loss or detecting the faint RF emission at the same frequency; thelatter is Fourier transform ICR [54]. When neutral reactants are introduced to the cell atlow pressures (1O torr) the ion signal will decay in proportion to any chemical reaction.In order to have better selection of the reacting ions, the tandem-ICR was developed [53]8in which there is a source ICR cell for production and selection of the desired ions, anda reaction cell where those ions react with some other species. Between the two cells,the ions are accelerated through a mass selector, decelerated, and velocity-selected by aWein filter2 so the reacting ion and reaction energy are well characterized; the energiesare not generally in a thermal distribution, but can be controlled from below 0.1 eV toseveral keV. Reaction times are from just a few to hundreds of milliseconds, and pressuresmust be very low, i0 torr. Detection of products is possible by ejecting ions from thecell with a pulsed electric field.In order to measure truly thermal reaction rates, higher pressures are needed, whichleads to the flow-tube methods. In a flowing-afterglow (FA [50]) a flowing gas mixture orpure carrier gas is ionized to a weak plasma or “afterglow” by electric discharge. (Someother gas may be injected downstream to create the desired ions if the carrier gas aloneis ionized.) After the ions have some time to be collisionally thermalized in the ‘‘ 1 torrflowing carrier gas, a reactive gas is introduced. At the end of the flow tube (which takesmilliseconds to traverse) is an orifice leading to a high-vacuum mass spectrometer whichmonitors the reactant and product ions. Reaction rates are measured by varying the flowrate of the carrier or the injection point of the reactant. The main disadvantage of the FAis that the afterglow may contain many reactive species, including free electrons and manydifferent ions, whose presence makes product detection difficult, and with side-reactionsthat obscure the reaction of interest.The SIFT (selected ion flow tube) method [46,50,55] works like a FA, but the afterglow plasma must pass through a quadrupole mass filter and the selected ions are injectedinto a fresh stream of carrier gas to then react with an injected reagent. This not onlyprevents unwanted reactions, but facilitates much better product analysis. Like a FA, thereactants are well thermalized (80—600 K) in the 0.1—1 torr bath gas, typically flowing at2 See the discussion of the beam “separators” in section 1.4.930 rn/s for a reaction time of 50 ms.Both SIFT and FA devices may be converted to drift tubes by fitting them with electrodes to continuously accelerate the ions as they are swept down the tube by the carriergas. These devices are used to investigate non-thermal (fraction of an eV) reactions.To measure reactions at very low temperatures, there is the CRESU apparatus [56,57],in which a gas mixture is expanded through a nozzle to form a low-pressure (5 x i0 to0.1 torr) supersonic (mach 2—5) jet with a temperature of 8—80 K. Ionization happensby electron impact in or shortly after the nozzle. Since no ion selection is performed, thismethod may suffer from the same deficiencies as the FA.This thesis introduces a new technique to the field: iLSR. The Muon Spin Rotationmethod is outlined below, but some important differences with the usual ion chemistrytechniques must be mentioned. Since uSR observes only species containing a muon, itcannot be used for most ions, but it is ideal for studying the muon analogs of protonatedions. These muonated ions are not produced by ionization of a neutral molecule, but bystopping a beam of positive muons in an appropriate gas mixture so the associateswith the moderator gas to form for example HeMu+, NeMu+, ArMu+, or N2Mu+, whichmay then react with other gases present. There is no debris of electron bombardment tocause problems, although at very high densities the radiolysis track left by the mightcome into play [38,39,58]. Reactions are monitored by the disappearance of the reactant,or, more correctly, by the loss of the muon spin polarization. The time-scale of reactionis short, on the order of microseconds, limited by the 2.2 ts radioactive lifetime of themuon, but that is still plenty of time for full thermalization as the pressures employed are1 atm or greater—much higher than in other ion—molecule reaction studies. In comparingSIFT with ,uSR, the factor of 1000 shorter reaction time is matched by the factor of 1000increase in pressure.101.3 Protonated and Muonated GasesAs mentioned above, protonated ions are an important class of molecular ions, of interestastrochemically and for setting bacicity scales. The measure of a molecule’s gas phasebasicity is its proton affinity (PA), which is high for all neutral atoms and molecules.Triethylamine, for example, has a PA of 975 kJ/mol (10.1 eV), and water’s is 697 kJ/mol(7.2eV), and even helium has a PA of 178 kJ/rnol (1.84eV). To put these in perspective,the Boltzmann factor for deprotonation of H3O (at 200 C) is l0_88, which implies thereis not one free H+ in the world’s oceans, and, moreover, there never has been! Even inhelium and neon (PA = 2.08 eV) there is essentially no chance that a proton will remainunbound, and the same is true for a positive muon.The protonated rare gases have been the subjects of several theoretical and spectroscopic studies, although the first spectrum (of HeH [59]) was not measured until 1979.Calculations of potential energy curves and vibrational states for HeH+ [60—62], NeH+[63—65], ArH [64—66], KrH [65], and N2H [67] agree well with potentials determinedfrom elastic scattering [68,69] and with the measured spectra [59,70—74], as should beexpected for these relatively simple ions.The potentials for the muonated ions are essentially the same as for their protonated counterparts, with little break-down of the Born—Oppenheimer (BO) approximation—while Mu is much lighter than H, it is still very much heavier than an electron.Figure 1.1 shows the potential for NeMu (NeH, from [65]) and for the unbound NeMu(NeH, from [76]); the energy difference at large separations is 13.6 eV, the ionization potential of H (Mu). Also shown is the attractive Langevin charge—induced-dipole potentialfor NeMu (see chap. 3). For both HeH and NeH, the Langevin potential matchesthe ab initio potential neither at short range (which is not surprising) nor at long range(see inset of figure 1.1) where better agreement could be expected; but calculations forAr + 112 show Langevin behavior beyond 4 A [77]. Perhaps the low polarizabilities of—‘ —4>ci)>‘ —6CUJ_8—10—121120—2—141 2 30 4r(Ne—Mu) (A)Figure 1.1 Potential energy curves for NeMu and NeMu with the vibrational energylevels for NeMu+ [75] (which are clearly anharmonic). The zero of energy is for separatedNe + Mu. The dashed line is the charge—induced-dipole potential for Ne—Mu, whichdoes not accurately match the calculated potential at either short or long range (inset).Vertical transitions are shown for the neutralization of NeMu+ from v = 0 and 1; theseshow how excitation increases the exothermicity at both ends of the transition, as longas it is vertical (see discussion in section 5.2).12He and Ne make the Langevin potential a poor approximation at any distance, or morelikely, the detailed calculations are not very accurate at large separations, although theab initio potential of Kolos and Peek for HeH [61] is claimed to be good out to 4.5 A [61].Fournier, Le Roy, and Lassier-Govers [75] applied a slight BO correction to the Kolos potential (which is BO-approximate) to give the HeMu potential, but the energy differenceswere very small.In contrast to the potentials, the rovibrational energy levels are very different fromthose of the protonated ions: due to the low mass of muonium, the rotational and vibrational energy spacings, including the zero-point energies, are approximately three timesgreater than for the protonated ions. Fournier and co-workers [75] have determined theenergy levels and lifetimes of the rovibrational states of HeMu+ and NeMu+, using thepotential of Rosmus and Reinsh [65] in the latter case, and these are reproduced intable 1.2. Approximate values for the (D0) binding energies have also been calculatedby Wedlich et al. [78]. There are only 5 bound vibrational levels in NeMu (shown infigure 1.1), 4 in HeMu, and 8 in ArMu, compared with 10 for both NeH and HeH,and 24 for ArH+ [61,78]. The sparseness of these states may be an important factor inany rovibrational excitation and quenching of these ions [79].Besides giving widely spaced vibrational levels, the low mass gives a much highervibrational zero-point energy for any Mu-bearing molecule or molecular ion. The difference in zero-point energy at the transition state makes some reactions much slower forMu than for H [82], but such effects are expected to be unimportant for ion—moleculereactions. Zero-point shifts for muoriated molecular ions reduce their binding energiesbelow their protonated counterparts, which can seriously alter the energetics of a reaction involving a muonated reactant or product. Table 1.3 gives the binding energies andzero-point shifts for the muonated gas ions studied in this thesis. There have been nocalculations of the energy levels in N2Mu+, so the binding energy was calculated fromthe N2H value of 5.13 eV [67] by subtracting an estimate of the difference in zero-point13Table 1.2Rovibrational Energy Levels and Predissociation Lifetimesa of HeMu and NeMu [751HeMu+ J v=0 v=1 v=2 v=30 —1.5195 —0.7252 —0.2191 —0.01661 —1.4634 —0.6830 —0.1923 —0.00862 —1.3544 —0.6010 —0.1420 0.0021 (2.56 x 10—’)3 —1.1964 —0.4841 —0.07434 —0.9967 —0.3395 —0.00155 —0.7634 —0.17706 —0.5066 —0.01087 —0.2377 0.1303 (3.32 x8 0.0291 (3.51 x i0)9 0.2689 (5.31 x 10’s)NeMu+ J v=0 v=1 v=2 v=3 v=40 —1.7863 —0.9750 —0.4026 —0.0836 —0.00231 —1.7524 —0.9476 —0.3824 —0.0723 —0.00032 —1.6850 —0.8934 —0.3428 —0.05083 —1.5853 —0.8137 —0.2852 —0.02194 —1.4550 —0.7100 —0.2119 0.0080 (7.92 x 10’s)5 —1.2963 —0.5849 —0.12626 —1.1118 —0.4414 —0.03347 —0.9050 —0.2835 0.0561 (2.78 x 10’s)8 —0.6795 —0.11649 —0.4398 0.0523 (9.16 x 10’°)10 —0.1912 0.2071 (6.46 x 10’s)11 0.0595 (4.22 x 106)12 0.3013 (7.62 x i0’)a Energies are given in eV with zero being separated He (Ne) + Mu+, predissociation(tunnelling) lifetimes are given, in seconds, for quasibound states.14Table 1.3Binding Energies and Zero-Point Energy Shifts for Muonated Ions.Ion LZPE statesb refHeMu 1.53 0.31 4 10 61,75NeMu 1.79 0.29 5 10 65,75,78ArMu 3.57 0.27 8 24 78N2Mu 0.40’— 67,80H2Mu d 0.39 81a ground-state binding energies and the difference in Mu and H zero-pointenergies; given in eV.bnumber of bound vibrational states for MMu+ and MH+ (respectively).there are no calculations for N2Mu+, so the zero-point correction (LzPE)was taken from the vibrational frequency of N2H+ [80], and this was usedto calculate D0 for N2Mu from the N2H binding energy [67].dH2M11+ was not observed. Since the trihydrogen ion cannot exist in J = 0,LZPE includes the J = 0 —* 1 excitation energy of H.energy, as given by the vibrational spacing of N2H [80].Besides the bound states, there are several quasibound states of HeMu+ and NeMu+(and probably the other ions as well, but these have not been calculated). However, thereare only two with substantial predissociation (tunnelling through the rotational barrier)lifetimes: the HeMu v = 0, J = 8 state at +0.029 eV with a lifetime of 3.5 x i0 s andthe NeMu v = 0, J = 11 state at +0.060 eV which lasts 4.2 x 10_6 s [75]. (The HeMulifetime estimate was reduced from the value of 3.4 x 106 s calculated initially [75], andsince the NeMu+ lifetime was not recalculated, it may be lower as well.) Radiative lifetimes for all rovibrational states of HeMu+ were calculated, and the shortest lifetime was36 1us (v = 1, J = 0); much longer than the muon’s radioactive lifetime, but marginally15accessible to a 1uSR experiment. Except for v = 0, higher J states have longer lifetimes.1.4 Muon BeamsThe properties of muonated rare gases have now been described, and related to theirprotonated counterparts. Also, the SR technique has been mentioned, without sayingwhat it measures, or how. The remainder of this chapter seeks to answer these questionswhile providing an introduction to the jiSR method.Muon production begins with the acceleration of particles such as protons to energiesabove 145 MeV by a particle accelerator (man-made or cosmic). For instance, the TRIUMFcyclotron, where these experiments were performed, produces a beam of 500 MeV protons.When such a beam collides with a target, many types of particles are created, but theones of interest here are positive pious. Pions are the lowest-mass mesons and, like allmesons, are short-lived, decaying with a mean life of 26 ns through the process(1.4)which is exoergic by 34 MeV and produces a 4.1 MeV j in the pion rest frame. Moreimportantly, it is a parity violating process producing muons with 100% negative helicity(their momentum and spin vectors are opposed). This happens because the neutrinoproduced, like all neutrinos, must have negative helicity, and since the pion has zerospin, angular momentum conservation forces the muon to have negative helicity as well.(Negative muons formed by r —f i + have positive helicity.) All uSR (for “muonspin rotation” or “relaxation”) experiments depend on this well-defined muon spin.For the experiments presented in this thesis, a surface beam was used [83], forwhich muons are produced by the decay of pions at rest on the surface of the productiontarget. Surface muons form an essentially monoenergetic 4.1 MeV beam with 100% longitudinal spin polarization. This beam is collected, focused, and momentum-selected bya series of magnets and other devices which form the secondary beamline; in the case of16these experiments, the M2OB or M15 channels at TRIUMF. Figure 1.2 shows the layout ofthe M15 channel which was specially designed for surface muon beams, and commissionedduring the early stages of this thesis work by myself and others, similar to our earlier workon the refurbished M20 [84].As the experiments of this thesis usually involved gases, such as helium, with verylow muon stopping power, the momentum selection of the beam was critical. Muonsthat scatter from the entrance window or pass through the gas without stopping give adiamagnetic signal when they are stopped in the sides or end of the aluminum targetvessel. This is an insidious background because the signal of interest is also diamagnetic.Selecting a narrow range of momenta minimizes the variations in stopping distance inthe gas and so minimizes the unwanted diamagnetic “wall signals.” Both the M20 andM15 channels possess movable slits placed at a dispersed-momentum focus, as well asspin rotators which act as velocity selectors, allowing these experiments to be run withLip/p < 5%. Nevertheless, the wall signals were often a problem; but one that could havebeen much greater were it not for the spin rotators on the secondary beamlines.It was found in some early studies for this thesis, given the typical experiment geometry at that time with a magnetic field perpendicular to the beam direction, thatwall signals exhibited a short lifetime and hence were indistinguishable from the relaxingmolecular ion signals under study. With such a configuration, no wall signal at all couldbe accepted. While some measurements of Xe in Ne [27] were successful, measurementsin He were difficult to impossible. However, with the magnetic field applied along thebeam direction, wall signals became long-lived, presumably because of the greater fieldhomogeneity around the circumference of the target vessel in this orientation. In thissituation, the wall signal contributes to any other long-lived signal, and the measurednon-relaxing amplitude is easily corrected by subtracting the wall signal amplitude. Inprinciple, such a longitudinal field could focus the muon beam slightly as it slows in thegas. Most of the experiments in this thesis involved transverse field jtSR, in which the17Figure 1.2 The M15 beamline at TRIUMF. This beamline is specially designed for(low-energy) surface muons, and uses a train of magnetic quadrupoles (Q) and dipoles (B)to deliver muons to the experiment. It rises above the muon production target 1AT1,and climbs to ground level, as it needs no heavy shielding. Its length eliminates pioncontamination, and the dual separators/spin-rotators eliminate positron contamination.The spin rotator is split, with a triplet of quadrupole magnets in the middle, to reducebeam dispersion at full spin rotation.Q12-Q14 TARGETLOCATION(EL. 291.5’)2BEAMLINE M1518muon spin was perpendicular to the magnetic field direction, but wall signals demandedthat the magnetic field be parallel to the beam direction; thus it was necessary to rotatethe muon’s spin from its natural orientation, through 900, to make it perpendicular to thebeam direction. This was accomplished by passing the beam through a spin rotator [84]:a box containing crossed magnetic and electric fields. If it were not for the electric field,the magnetic field would bend both the muon beam and the spin vector through 90°,but the electric field cancels the beam deflection, leaving only the spin rotation. Thespin rotator provides two additional benefits: it reduces the momentum spread of thebeam because the electric field exactly opposes the magnetic field oniy for particles of aparticular velocity (it is a Wein filter), and it removes positron contamination from thebeam as positrons have much higher velocities than muons of the same momentum.1.5 Muons in GasesWhen a muon exits the beamline and enters the tSR apparatus, it is not ready to participate in chemical processes as it still has 3—4 MeV (not meV!) of energy. The processof a muon slowing down in gases can be roughly divided into three stages or energyregions [85,86]: Bethe—Bloch ionization, cyclic charge exchange, and thermalization. TheBethe—Bloch regime occurs above roughly 100 keV and is characterized by the loss ofthe muon’s kinetic energy through the ionization and inelastic excitation of moderatoratoms [87].At energies between 100 keV and 20 eV, the undergoes a series of charge changingcollisions with the moderating gasMu+M(1.5)Mu+Mdetermined by the electron loss (o) and capture (urn) cross sections as well as by theenergy moderation cross section for the specific gas. In a high-IP gas like He, there are19approximately 80 of these cycles before cyclic charge exchange ceases due to a markeddecrease in the neutralization cross section below about 100 eV [85,86], although thethreshold for Mu formation is only about 14 eV. If the medium has a lower ionizationpotential than Mu (13.53eV), the threshold for electron loss is reached at 10eV, whereasmuonium formation is exothermic and can continue even after cyclic charge exchange hasceased. In the absence of chemical reactions, one would expect 100% muonium formationfor such gases. It takes about 15 ns [88] for a muon to be slowed from 3 MeV to the10 eV typical of final Mu formation in 1 atm of Ar [85]. After the charge exchange regime,other thermalization processes dominate: moderator excitation, elastic scattering, andhot atom/ion reactive collisions. These processes then dictate the ultimate thermalizationof the muon.While the effect of pressure, or the time between collisions, upon the muon polarization is negligible for Bethe—Bloch ionization, it is of considerable importance in thecharge exchange regime. Since electrons in the moderator are unpolarized, whereas theis polarized, muoniurn forms equally in two spin states, kie) and cv,j3). TheIe) state is an eigen-state of the IL+e hyperfine interaction, but the Ia,Be) state is asuperposition of the singlet and M = 0 triplet eigen-states and hence is not a stationarystate. In this case then, the muon polarization oscillates between e) and ae) at thehyperfine frequency, v0 = 4.5 MHz. Consequently, the lost polarization (PL, or ‘missingfraction’) will be significant if the period of cyclic charge exchange cycles is comparableto 1/v0 = 0.22 ns, or longer. Since the thermalization time is inversely proportionalto pressure, L will increase as pressure decreases. This effect sets a minimum workable gas pressure of -- 300 torr [85,89,90]. In most gases, there is no loss of polarization(signal loss) for pressures of one or a few atmospheres [85,89], although there are notableexceptions [89,91]. At much higher pressures, the ionization in the muon’s radiolysis trackmay be near enough to interfere, causing additional depolarization [38,39,58], althoughthere is no intrinsic upper limit on the density of targets that can be investigated by20ILSR [31,38,92].Emerging from cyclic charge exchange, a (small) portion of the muon ensemblepolarization has been lost (FL), and the rest is distributed between bare muons (PD)and muonium atoms (FM; D + Mu + L = 1). Most molecular gases have lowerIP’s than Mu, so 100% Mu formation would be expected, but in all molecular gasesstudied to date, there is a significant diamagnetic component of polarization [38,89,90],indicative of hot atom reactivity. Chemical reactions of translationally ‘hot’ Mu (e.g.,Mu* + C2H6—* MuH + C2H5) convert muonium to diamagnetic species, thereby depleting‘Mu and correspondingly increasing D• The study of such hot-Mu reactions is a richand ongoing field of research [89,90,93].In a pure inert gas, and even in an inert gas doped with a small quantity of molecular gas, hot atom reactions are not expected to be important because any Mu thatemerges from the charge-exchange regime will collide mainly with the inert bath gas. Ina high-IP moderator like He or Ne no Mu is formed from charge exchange, but the barecan undergo its own reactions. Even helium and neon have muon (proton) affinities> 1.5 eV [see §1.3 and ref. 75] so they will be muonated (protonated) in the three-bodyprocessMu + He --* (MuHej* (1.6)where Mu+ is just a bare muon, and the product is shown as vibrationally excited becausethe entire binding energy is unlikely to be carried off by just the one moderator collision.The problem of energy disposal impiies that the association occurs at low u+ kineticenergies, < 1 eV.While the final thermalization of Mu is quite inefficient [91] due to its low mass andresulting small energy loss per collision, kinetic studies [29,30,82] show thermal behaviorfor Mu at times 0.1 is. The charged is expected to thermalize more quickly thanMu due to higher collision cross sections [94]. However, a muonated molecular ion has21a mass almost equal to the moderator gas and so loses, on average, half its energy percollision. Once formed, molecular ions thermalize very rapidly.1.6 Muon Spin RotationAfter the muon beam has stopped in the gas of interest, the muons decay with a meanlifetime of 2.2 ,us according to+ 1’e +i711, (1.7)emitting a positron preferentially along the muon spin axis [95]. For a perfectly polarizedensemble of muons, the spatial anisotropy of positron emission is given byN(O)/N = 1 + A cos9 (1.8)after averaging over positron energy (0.0—52.8 MeV) and where 9 is the angle betweenthe muon spin and the path of the decay electron. The technique of jSR relies on detecting the decay positrons and tabulating these decays in a histogram of positron countsvs. time. In this time-differential method, the muon that created each decay positronmust be unambiguously determined, necessitating that only one muon be in the targetat a time. This requirement is ensured by the electronic logic used in the experiment’sdata acquisition system. If all positrons were detected with equal efficiency, and themuon beam was 100% polarized, then A = 1/3 [96]. In practice, higher energy positronsare detected more easily while low energy ones may not even get out of the target, thebeam is somewhat less than 100% polarized, and the polarization may decrease with time(relaxation) so A is always treated as an empirical factor A0 multiplied by a relaxationfunction G(t) which describes the loss of polarization over time. Moreover, 9 may alsobe time-dependent (precession).In the simple case where there is no coherent muon precession, such as when themagnetic field is zero or it is aligned with the muon spin, 0 is constant, and the longitudinal field relaxation function is denoted G(t). Thus, the histogram of positron decays22is described byN(t) = N0 e_t/T [1 H- A0 G(t) cos 0] + b (1.9)where N0 is a normalization, b is a time-independent background due to random events,T is the mean muon lifetime (2.2 us), and t is the time the muon spent in the targetbefore decaying. The subscript z identifies the relaxation as longitudinal or T1 relaxationin NMR parlance.However, the experiments for this thesis were performed with a magnetic field applied perpendicular to the muon initial spin direction. In this case, the muon precesseswith a characteristic Larmor frequency until it decays. The resulting variation of 0 withtime is seen as oscillations in the muon decay histogram, of which a typical example isshown in figure 1.3 for stopped in neon. Such a simple spectrum is described by theequationN(t) = Noe_t/T [1 + ADG(t) cos(c0+ D)] + b (1.10)N0e[1 + A(t)] + bwhere WD is the Larmor angular frequency for muons in diamagnetic environments= 85165 s’G’), and q is the initial phase angle between the muon spin andthe direction of the detector; + c’D is 0 in equation (1.8). AD is the initial amplitude for the diamagnetic precession, equivalent to A0 above. The relaxation function,describing transverse field dephasing in analogy with T2 relaxations in NMR, is here denoted G(t). In the gas phase, relaxations are generally simple ‘Lorentzian’ exponentialdecays (G(t) = e_t) due to chemical reactions or spin exchange. The relaxing oscillations constitute the signal of interest: the precessing decay asymmetry A(t), oftendenoted S(t). A representative “asymmetry plot” is shown in figure 1.4, and such plotswill be used for illustration through the remainder of this thesis.232000015000100005000C00,C0C-)00.0 1.0 2.0 3.0 4.0 5.0Time / p.s (20 ns per bin)6.0 7.0 8.0Figure 1.3 tSR histogram for 800 torr neon. The points represent the number ofpositrons counted within each time bin, (20 ns wide for the plot, but only 2.5 ns in theraw data) and the curve is the fit to equation (1.10). The error bars are due to Poissoncounting statistics alone: u = but they are smaller than the squares so are notvisible.—tI I I I I In0.350.250.15—0.15—0.25—0.350.0iilivii :1:1.0 2.0 3.0 4.0 5.0 6.0 7.0Time / p.s8.0Figure 1.4 The corresponding asymmetry plot, giving A(t) vs. t. The error barsinclude the uncertainty in the values for N0 and b and are shown on every tenth point.They increase at later times due to the low statistics after many muon lifetimes. Thevery slow signal relaxation of A = 0.03 its’ is due to magnetic field inhomogeneity.24The above is an over-simplification, however. As discussed earlier, the muon maywind up in any one of many different magnetic environments: diamagnetic, paramagnetic, or a host of others relevant oniy to the solid state [97], so equation (1.10)could be extended to include many precession terms, but only two terms are of interest for this thesis. Since the molecular ions studied are diamagnetic, the most important term is given by equation (1.10) above, for it applies to all muons in diamagnetic environments (D); the few-parts-p er-million frequency differences for variousdiamagnetic species cannot generally be resolved by tSR, which is limited to a frequency resolution of 0.5 MHz by the short muon lifetime. More accurate frequencymeasurements have required special techniques [98]. The other environment of interest is the paramagnetic muonium atom. In most substances other than metals, themuon will take an electron from the moderator to form muonium, as outlined earher. While muons in diamagnetic environments are coupled oniy to the field (ignoring small chemical shifts), the muon spin in muonium is coupled to both the external field and the electron spin. The details of the time dependence of muon precession in muonium are tedious but straightforward, and are treated well elsewhere[97,99]; and a simplified view of Mu precession is all that is needed for this thesis.For the case of polarized muons meeting unpolarized electrons at low magnetic fields,muonium atoms are formed equally in each of two ensembles: those with parallel spinsand those with opposed spins. Muoniuiii with opposed spins (sometimes loosely referredto as “singlet” Mu, but here termed “antiparallel”) is a mixture of singlet and tripletstates for which the muon spin direction oscillates at the magnetic hyperfine frequencyof 4463 MHz—too fast to be resolved by most iiSR apparatuses, although it has beendirectly measured in a high resolution experiment [100]. Parallel (or “triplet”) Mu is amixture of triplet states in a weak ( 10 0) magnetic field, and the muon spins precesscoherently with essentially half the electron’s magnetic moment in the opposite sense to25diamagnetic precession and with a frequency WMu 103 times higher than WD. The LSRspectrum at low fields is thus described byN(t) = Noe_t1’T [1 +ADG,D(t) CO5(WDt+D)+AMuGr,Mu(t) cos(—wMUt+qMU)] +b (1.11)where the new parameters are analogous to those in equation (1.10). The asymmetrysignal for such a histogram is shown in figure 1.5.Mu is not the principal focus of this thesis, so very few runs were taken at lowfields. The main interest is in reactions of diamagnetic ions as revealed by diamagneticsignal relaxations, G,D(t), which are more clearly visible at higher magnetic fields withproportionately higher Most runs were performed at the highest field attainable withthe gas chemistry apparatus described later, 300 G. At such fields, Mu is split intotwo frequencies [97], but both are too high to be seen with most 1aSR apparatuses. Thus,equation (1.10) describes the bulk of the tSR data for this thesis.0.20.0SS>%Co< -0.1—0.20.0Figure 1.5 The asymmetry signal, A(t) vs. t, for 1 atm nitrogen. The small diamagnetic precession (AD = 0.036 vs. AM = 0.10) is visible as a slow shift in the Mu precession.The Mu relaxation rate of = 0.15 11s is slightly faster than the diamagnetic relaxationin figure 1.4 because the faster (even at the applied field of 5 0) Mu precession exacerbatesthe problem of magnetic field inhornogeneity.1.0 2.0 3.0 4.0 5.0 6.0Time / ,us261.7 Relaxation FunctionsThe most important quantity measured for this thesis is the relaxation of the iSR signal. This is not apparent from figure 1.4, which displays a signal undergoing almost norelaxation, but is much clearer in figure 1.6 and in the corresponding figures in chapter 4where the results are reported. In general, the relaxation functions G(t) and G(t) takemany forms, depending on the physical mechanisms of relaxation. In the solid state, forexample, relaxation functions are often Gaussian but may take many other forms [97,101].In the realm of gas phase chemistry, however, there is oniy one3 relaxation function ofinterest: the exponential relaxation, G(t) et, whether in a longitudinal (Ge) or transverse (Gm) magnetic field. That is not to say that muons exhibit a Lorentzian distributionof precession frequencies, just that the oscillations are damped by a simple exponentialdecay.In transverse magnetic fields, chemical reactions relax SR signals by changing themagnetic environment, and so the precession frequencies, of muons at random times. Themost common case, exploited in studies of Mu kinetics [29,30,82,99,102,103], involves reactions of the Mu atom to form diamagnetic products. The reverse also works: reactionsof diamagnetic species (molecular ions) to form Mu or some other paramagnetic speciesare manifest as relaxing diamagnetic signals, as illustrated, for example, in figure 1.6showing the reaction of NeMu+ with NO. Regardless, the necessary condition is thatthe muon precession frequency be changed incoherently on a time scale greater than thereciprocal of the difference in frequency. For reactions Mu —* D and D —f Mu, this conditionis met when the reaction is slower than one period of Mu precession. With this simpletransverse field relaxation mechanism, and concentrating on the case of principal interestThis is not strictly true, depending on what is “of interest.” An obvious exampleis relaxation due to inhomogeneity of the applied magnetic field; the distributionof fields over the stopping distribution of the muon beam is almost certainly neverLorentzian.27to this thesis, a diamagnetic reactant (D) forming Mu, the relaxation function is givenby the fraction of reactant remaining at any time,G(t) = [D]/[DJ0, (1.12)where square brackets denote concentration or density.4 Thus, the relaxation function isgiven directly by some kinetic mechanism.The preceding is not exactly true because the muon spins may be dephased by processes other than chemical reaction. It was noted above that magnetic field inhomogeneitymay cause non-Lorentzian relaxation; however, if the inhomogeneity is low, making therelaxation rate low, the deviation from a simple exponential is very small. This is thesituation for this thesis, as illustrated by the almost-non-relaxing signal in figure 1.4. Themuonium relaxation in figure 1.5 is slightly faster due to the higher precession frequency,but it is still apparently exponential. As long as such systematic relaxations can betreated as exponential, they may easily be accounted for.Since only a few million muons are used per experiment, and only one muon isallowed in the target at a time, the muons are near infinite dilution and the kinetics formuon chemistry are invariably pseudo-first-order:[D]/[D}0 = = G(t). (1.13)In the absence of background relaxation, the relaxation rate ) is identified with thepseudo-first-order rate constant. For the second-order reaction D + X —* Mu + Y, with arate coefficient k,= k [X} + )(O). (1.14)where the terms k [X] and )(O) give the pseudo-first-order rate constant and a backgroundrelaxation respectively. More complex kinetic schemes may give more elaborate relaxationfunctions, but they will always be built of exponential relaxations.“ Units of number density are used for concentrations in this thesis.28Time / sFigure 1.6 The relaxing asymmetry signal seen in neon with 6.74 x 1014 moleccm3of added nitric oxide. This is actually an unusual relaxation shape for this thesis—two-component relaxations were usually observed. The relaxation is due to the formationof paramagnetic Mu and maybe to formation of paramagnetic NOMu+, as discussed inchapter 5.0.350.250.15> 0.05I.a)E —0.05E>%—0.15—0.25—0.350.0 1.0 2.0 3.0 4.0Time / /.Ls5.0 6.0 7.0 8.0Figure 1.7 Two-component relaxation seen in 800 torr neon with 22.5 x iO’4 moleccm3 of added CF4. The interpretation of the fast and slow relaxation rates, and their0.350.250.150.05—0.05—0.15—0.25—0.350.0>‘-4-,a)EE>%U)1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0amplitudes, is left for later chapters.29Anticipating the results to be given later, the 1uSR histograms for molecular ion reactions typically give relaxing asymmetries that look like figure 1.7 showing the signal forNe doped with CF4. These were analyzed using a relaxation function of the formAD G(t) = A1 e1t + A2 eA2t (1.15)The interpretation of this, to be discussed later, is based on a model of competing reactions, only one of which causes depolarization.Chapter 2EXPERIMENTAL TECHNIQUESThe rare gas molecular ions studied for this thesis were prepared simply by directingpositive muons into a target vessel filled with the appropriate inert gas moderator: hehum, neon, argon, or nitrogen. Ion—neutral reactions were induced by doping the raregas with a few parts-per-million of a reactive gas, the neutral species. These formationand reaction processes were investigated by monitoring the muons’ magnetic environmentthrough the technique of jzSR.2.1 ApparatusThe layout of the tSR apparatus is shown in figure 2.1. It consisted of a large targetvessel mounted on a cart between Helmholtz coils and arrays of scintillation counters.The upper scintillators were moveable vertically so as to accommodate the varying sizesof target vessels; for the large molecular ion gas target, the scintillators were raised fully.The target vessel and collimator could be rolled independently along rails and the wholeapparatus could be rolled in tracks on the floor. This allowed the target and collimator toremain fixed in space while the coils and counters were repositioned along the line of thebeam to match the muon stopping distribution. Generally, though, the beam momentumwas varied to adjust the muon stopping distribution so the center of the coils could beplaced near the center of the target.3031A AC____________I•1. I I___ft,uFGEuICFigure 2.1 The ,uSR gas chemistry apparatus. The Helmholtz coils (A) are orientedfor spin-rotated muons, giving a 300 0 magnetic field in direction B. There are bothupper and lower positron counter arrays (C), each with three scintillators and graphitedegrader (D). The target vessel (E) is shown without its variable-temperature insert.The spin polarized (ft) muon beam (F) traverses the evacuated beam-pipe (G), passesthrough a brass collimator (H), triggering the thin muon counter (I), before entering thetarget through a thin Kapton window (J). The muons stop near the center of the target,retaining most of their initial polarization. Each muon precesses (out of the plane of thepage) until it decays, emitting a positron which may be detected by one of the counterarrays (C).32The main 1.5 m diameter Helmholtz coils provided magnetic fields from 0 gaussto in excess of 300 gauss oriented horizontally, and homogeneous to ‘- 1% over a 5 litrevolume. There were also two other pairs of coils, capable of generating a few gauss, whichwere used to accurately zero the field and to provide a weak vertical field when necessary.A single thin (0.025 cm) scintillator placed between a beam collimator and the target served as the incident muon counter. Two arrays of three 0.6 cm thick scintillationcounters placed above (Top) and below (Bottom) the target—at right angles to boththe field and the beam directions—were used for detecting decay positrons. Each arrayconsisted of two 25 cm x 45 cm scintillators, followed by 2.5 cm of graphite degrader andone 41 cm x 45 cm scintillator. Sometimes, such as when using the variable temperatureinsert (see below) which slowed the emitted positrons, or when one counter was weak,only two counters of three were used. A positron decay was detected by simultaneouscounts in all three (or two) counters of an array.The reaction/target vessel used for room-temperature measurements was a 174 litrehollow aluminum cylinder: 90.4 cm long by 49.5 cm in diameter. The large volume wasnecessary because the low stopping power of helium would allow muons to reach the wallsof a smaller vessel, giving rise to unwanted diamagnetic signals. The muon beam enteredthrough a thin (0.25 mm) Kapton window at one end of the “can.” At the other end wereinlet and pumping ports for the gas samples.For experiments not conducted at room temperature, the big can was fitted withan insert as shown in figure 2.2. The space between the insert and the outside shellserved as an insulating vacuum jacket; it contained aluminized mylar heat shields, andwas continuously pumped on. The insert had a central sample volume of 75.4 litres(73.7 cm long x 36.1 cm in diameter) with a 0.025 mm stainless steel window. A plasticinner window was used at first but was abandoned because in those runs carried out withhelium as moderator, too much He diffused through it, ruining the insulating vacuum.The muon beam entered the gas by first passing through a 0.125 mm Kapton window33Figure 2.2 Diagram of the variable-temperature target vessel. Legend: A) thermalexchange gas inlet, B) vacuum jacket pumping port, C) sample gas inlet/outlet, D) thermocouple in pressure-tight tube, E,) exchange gas outlet, F,) Viton 0—rings, G) 0.125 mmKapton window, H) Teflon 0—ring, I) 0.025 mm stainless steel window, J) stainless steelwire support, K,) aluminized mylar heat shield (perforated for easy pumping), L) insulating vacuum jacket, M) thermal exchange gas space, N) sample gas space.1034in the outer shell, traversing the vacuum space, then passing through the inner steelwindow. In order to prevent leaks at low temperatures, the inner window was sealedagainst a Teflon 0-ring, which remained pliable in the cold; and aluminum screws wereused to hold the aluminum flange against the window. In fact, the window did leak whencooled down, but that was easily fixed by removing the outer window and tightening thescrews while cold.The insert was double-walled on the sides, allowing the sample gas temperature tobe varied by flowing pre-heated or chilled air in the space between the walls. Compressedair was first dried by flowing through a room-temperature zeolite moisture trap, andthen either heated by an electric (Chromalox) heater, or cooled by flowing through a coilimmersed in liquid nitrogen. The sample temperature, as monitored by a thermocouplein a sealed tube projecting into the central volume, was controlled by adjusting the flowrate of the exchange gas. In first use, the lowest temperature attained was —100°C,but after the installation of the heat shields (and a steel inner window) the vessel waseasily cooled to —170°C. Temperature homogeneity along the insert was excellent, lessthan 1°C, so temperature errors were dominated by variations over the time needed for aseries of runs. High temperature runs were kept within a range of +3°C, while the moredifficult low temperature regulation gave a range of +5°C, with the fluctuations recordedon a strip-chart recorder. There was no temperature control for the “room temperature”runs, and some of these may have temperature errors in excess of ±5° C, although detailedrecords were not kept.2.2 Data AcquisitionThe data acquisition system was logically equivalent to what had been used in earlier gasphase jtSR studies at TRIUMF [102] and the details are given therein, but some simplifications and improvements have taken place, so it is worth giving a precis here of how thecurrent data acquisition system operates.35Figure 2.3 Logic diagram for iSR data acquisition. The signals proceed generallyfrom the top to the bottom of the picture, starting at the scintillation counters. Constant-fraction discriminators (CFD) are used for the thin counter (it) and the first counter ineach of the positron counter arrays (T or B) to give better timing. Scalers are not strictlynecessary but provide a quick indication of problems. The circles at the bottom arevarious inputs for the Le Croy TDC. A good event is recorded when all three counters ofan array fire after there has been a muon counted (data gate, 0), but only one muon(no pileup, ); and no subsequent muon (bit 0) or positron (bits 1, 2) is detected withinthe gate.(and)(fan—out)delay36Figure 2.3 gives the logic diagram for the signal processing used to collect the ,USRdata for this thesis; it is best understood with reference to the diagram of the apparatus,figure 2.1. A muon, upon leaving the beamline, passes through a collimator in a 2.5 cmthick brass shield and then through the thin counter. If there is no other muon in the target (i.e., the “pileup” gate is not already active), the discriminated counter pulse startsa high precision (125 ps time-resolution) Le Croy 4204 time-to-digital converter (TDC)or “clock”. (If there is pileup, both muons are rejected.) Within about ten nanoseconds,the muon has thermalized and precesses in the applied magnetic field until it decays,perhaps a few microseconds later, emitting a positron as discussed before. This positronmay pass through a triplet of counters and stop the clock. Then the clock writes thetime to a CAMAC-resident histogramming memory module, which increments the bincorresponding to the time of the decay in the histogram appropriate for the counter array(Top or Bottom). The clock resets if no positron is detected within a gate period of a fewmuon lifetimes, or if two (or more) positron “stop” signals are received before the datagate expires.In the original TRIUMF implementation for zSR data acquisition [102] almost all thegood-event filtering had to be done with NIM logic modules and an MBD microcomputer.This was not only more cumbersome, but missed some events while the computer wasbusy. Then, also, the histograms resided in PDP11 memory, a scarce resource neededfor networking software. In the present scheme, the histograms are periodically copiedfrom the CAMAC histogramming memory module to a file on the PDP11 computer, whichis subsequently copied to a VAX computer for analysis and backup. After the data acquisition for this thesis was completed, the PDP11 computer was retired, and now VAXcomputers are interfaced directly with the CAMAC modules.372.3 Data AnalysisThe data histograms were analyzed individually with a version of the non-linear, multi-parameter optimization program MINUIT [104]. Diamagnetic spectra were fitted by equation (1.10) with G given by equation (1.15) or (1.13); and the few low transverse field runswere analyzed according to equation (1.11). The best fit is determined by minimizing thechi-squarex2(N _f(t))2 (2.1)where f(t) is the appropriate expression for N(t), N is the number of counts in bin i,and u is its uncertainty. Given the Poisson counting statistics of these experiments,= In situations where the data was over-determined, one parameter was oftenfixed at its expected value. In particular, when the “fast” relaxation was quite slow at lowreagent concentration, the slow relaxation rate was usually fixed to a value determinedat a higher concentration.These were not the only fits necessary; the parameters determined by fitting a seriesof runs were subsequently analyzed in terms of various models, say y f(x). These fitstook account of both “x” and “y” uncertainties by minimizing the modified chi-square=2— f(x))22 (2.2)Uj + (f (x))where f’ represents the derivative of f and so converts o into an uncertainty in y uncorrelated with o,. When necessary, these fits were performed with a version of MINUIT [104],but the many linear fits were done with the modified linear regression outlined next.In the case of a straight line fit, y = f(x) = ax + b, the modified chi-square (2.2)may be written(yaxb)2(2.3)38The minimum of this x2 (and the best a and b) could be determined by a general-purposenon-linear fitting program like MINUIT, but the the approach used in this thesis was basedon the analytical linear regression [105]. The minimum x2 occurs where0 — ——2x(y— a; — b) 2aa(y — a; — 2 4— Oa — u + (auj2—[aj + (a)2]and25— ——“ o + (aoj2are simultaneously satisfied. For the case of cr = 0, these equations can be solved forboth a and b to give the familiar expressions for a weighted linear regression [105], but inthe present situation, the best that can be done is to solve equation (2.5) to give b as afunction of a. This is useful because it reduces the problem to that of numerically solvingthe single equation (2.4). This was accomplished easily and efficiently using the Newton—Raphson method [105]. This technique requires the full second derivative dt92/daOa andan initial guess for a. The derivative is easy to calculate analytically and the familiaranalytical regression provides an excellent initial guess. The partial second derivativesmust also be calculated to get the uncertainties in a and b.2.4 Reagent GasesThe bulk of each sample mixture was the moderator gas, usually He or Ne, but somestudies were also performed using Ar, H2, and N2. All of these were UHP grade, withquoted purities of 99.999%. Nevertheless, given the low concentrations of reagent addedto these gases, the impurities were significant; thus, the moderator gases (He, Ne, and H2)were further purified as they flowed into the target by passing them through a trap filledwith type 4A molecular sieve and cooled in liquid nitrogen. Before this cold trappingprocedure was adopted, values for ).(0), the molecular ion relaxation rate extrapolatedto zero concentration of reagent gas, were 1—3 [Ls’, but trapping caused a sharp decline39in these values to 0.3 jis’, but still varying between experiments. This effect will bediscussed in later chapters.Many of the reactant gases were of research grade (>99% pure), obtained in lecturebottles, and were used without further treatment. However, the low proportion of reactant gas used (-.l00 ppm) indicates that impurities in the moderator are of far moreconcern than reactant impurities.Some reactants were liquids under standard conditions, so they were poured intostainless steel sample bottles to use as sources of vapor. It was important to remove theair admitted to the bottle as well as air dissolved in the liquid, especially since air is selectively concentrated in the vapor phase and 02 rapidly depolarizes muonium through spinexchange [106]. To degas the liquid samples, the small steel bottle was immersed in liquidnitrogen to freeze its contents, it was evacuated and pumped on, and then the sample wasmelted and boiled by immersion in hot water or a flame. These freeze-pump-thaw cycleswere repeated at least three times, which, from previous experience [89], reduces oxygencontamination sufficiently, even for much higher vapor concentrations. This procedurewas followed even when only the diamagnetic signal was to be measured.To put the sample into the target vessel, a small measured volume (usually ‘—s 110cm3) was filled with the desired reagent gas, from either a lecture bottle or liquid samplebottle, up to a desired pressure (such as 100 torr) as measured on an MKS Baratrori capacitance manometer with 0.5% accuracy; then the sample was admitted to the evacuatedtarget vessel. Finally, the vessel was filled to the desired pressure with moderator gas,typically 1 atm or more of He, Ne, or Ar. In a typical experimental determination ofion—molecule reactions, four or more reagent concentrations were run in order to obtaina good fit to the bimolecular rate constant.Chapter 3THEORIES OF ION—MOLECULE CAPTUREREACTIONSThe dynamics of ion—neutral reactions are dominated by long range attractive potentials:charge—dipole, charge—induced-dipole, charge—quadrupole etc. These make it possible toignore the structural details of the reactants and calculate reaction rates from the long-range potential alone. Such calculations have been thoroughly reviewed [107—109] and alimited review is the purpose of this chapter. The common feature of all such calculationsis the concept of a capture collision by which the reactants that have less than some critical impact parameter are brought together and, in the absence of short range repulsion,pass through each other. The results of such calculations are often called “orbiting” crosssections, but that is misleading as the only orbiting trajectories are those with exactlythe critical impact parameter. “Capture” is the most common term, and is the one usedin this thesis, but it really is more applicable to the assumption that the reactants forma long-lived complex. The long-range potential in no way guarantees capture in thatsense, and moreover, “capture theories” do not require complex formation, only that reaction must occur when the reactants are drawn together. When “capture” is used here,complex formation is not implied. Perhaps the least misleading term is just “collision,”distinguishing between the calculated collision rate and the measured reaction rate.4041Even (or especially) when the capture assumption of 100% reaction efficiency fails,calculations of the capture cross section are important because the difference between thecalculated collision cross section and the measured reaction cross section gives an insightto the real dynamics of a particular reaction. Discussion of steric repulsion, additionalattractions, or energy disposition must begin with the calculated capture rates.3.1 Langevin Reaction RatesTheoretical rate constants for the reaction of a point charge with a polarizable molecule having no permanent dipole moment were derived by Gioumousis and Stevensonin 1958 [1101, and earlier by Eyring, Hirschfelder, and Taylor [111], and by Vogt andWannier [112], drawing from work done by Langevin at the turn of the century [113].The reaction is controlled by the long range charge—induced-dipole interaction, which hasthe potentialV(r) = —q2a/2r4, (3.1)where q is the charge of the ion and a is the isotropic polarizability of the molecule.Langevin calculated trajectories for collisions involving this potential, but the operationof ion—molecule capture is best seen by using the effective potentiallff+1orb, (3.2)whereL2 m2vb b2EEorb= 2 2 (3.3)2mr 2mr rwhich gives the “centrifugal repulsion” due to the orbital (non-radial) motion of the colliding pair; and where v is the relative initial velocity of the pair, E is the relative initialkinetic energy, mv2 b is the impact parameter, and m is the reduced mass. (The notation of this thesis is already over-burdened with n’s.) The distance of closest approach r042(i.e., the turning-point of the trajectory, as shown in figure 3.1) is simply the value of rthat gives = E in equations (3.2) and (3.3); if is always less than E, r0 = 0.The maximum in V occurs where aff/ar = 0, at the collision, or capture, orcritical radius= q2a/Eb2 (34)There is a critical impact parameter b for a given E, found by setting ff(r) = E andeliminating r0 to give= (2qo/E)4. (3.5)Trajectories with b b bring the reactants no closer than r = while thosewith b < b have the reactants, ideally, passing through each other. This discontinuityat b = b is clear in figure 3.1. If no reactions can occur at separations greater than r,and if trajectories bringing the reactants into close proximity always lead to reaction,1—////0 I0 1b /bFigure 3.1 Dependence of the Langevin distance of closest approach r0 upon theimpact parameter b, given in terms of the critical impact parameter b = (2qa/E)”4.Capture occurs for all impact parameters b < b. The dashed line at r0 = b shows therelationship in the absence of potential.43then the reaction cross section isu(E) = = K2q2a/E, (3.6)and the corresponding rate constant iskL = vo = 27rq%,/7. (3.7)This is the Langevin—Gioumousis—Stevenson rate constant and it is energy independent;there is no need to average over energy distributions, and kL is both the microscopicand macroscopic rate constant, independent of temperature. (The same result had beenderived in 1936 by Eyring et al. [111], but the derivation required a Maxwellian velocitydistribution, an unnecessary restriction.)The energy independence of kL must break down at high energies, when the captureradius becomes smaller than the radius of the “hard core.” However, the Langevin ratehas been used to predict reaction rates at 100 eV energies [114]. It can also fail becauseof changes to the long-range potential due to anisotropy of the polarizability or to otherlong-range interactions, such as radical—radical or charge—dipole attractions.3.2 The Locked DipoleThe case of an ion reacting with a molecule possessing a permanent electric dipole moment is more difficult. The potential depends on the angle 0 that the dipole makes withthe line connecting the colliding particles,aq2V(r) = ———i — ——cosO (3.8)where ltD is the electric dipole moment. It is the rotation of the dipole (variation of 0)that complicates the treatment of this system. If the dipole is assumed to have a fixedorientation, however, capture rates can be easily calculated.For 0 = 90°, the potential is the same as for a non-polar molecule [equation (3.1)above] and the capture rate is identical to the Langevin rate. This angle is not favored44so this result is unrealistic; but if the dipole is rotating very rapidly, such that its periodof rotation is much less than the collision time, its effect averages to zero—the case ofthe 900 locked dipole. So, anticipating more accurate treatments, it is clear that onerequirement for a proper description of ion—dipole reactions is that the predicted rateapproach the Langevin or 90° locked dipole rate at high temperatures.For 0 = 00 [115], the dipole interaction is at its maximum(3.9)Repeating the treatment of equations (3.2) through (3.5) gives= qfLD/E + 2cq2/E (3.10)which yields the microscopic rate constantkLD(E) = (3.11)This time, though, the rate constant depends on energy, and the microscopic rate mustbe averaged over the velocity distribution of the reactants to get the bulk rate. Sinceion—molecule reactions are often studied with mass spectrometers or ion flow tubes, thevelocity distribution used when taking the average must be appropriate to the particularapparatus used. However, taking the Maxwell—Boltzmann average gives the thermal rateconstantkLD(T)= (+ IDV’2/7T) (3.12)where k is Boltzmann’s constant (distinguished from rate constants by context) and T isthe absolute temperature.Unfortunately, the 00 locked dipole rate constant grossly overestimates experimentalrate constants. This is not surprising because the electric field of the ion is not strong45enough to lock the dipole into a fixed orientation at more than a few degrees Kelvin. Nevertheless, the 00 locked dipole rate constant does provide an upper limit on ion—dipolecapture rate constants.An empirical correction can be made to equation (3.12) by introducing a “dipolelocking constant” C which can have values from 0 to 1,(3.13)The value of C for a “Partially Locked Dipole” is determined by experimental data, andfor real systems is quite small, 3 0.2 [116].Equation (3.13) is a semiempirical formula, not really a theory of reaction and is oflittle predictive use. However, there are descriptions which try to evaluate C through aproper average of cos 0 in equation (3.1). Some of these follow.3.3 The Average Dipole Orientation TreatmentsThe average dipole orientation (ADO) theory of Su and Bowers [116] calculates averages1of cos 0 at a number of reactant separations which are then used in the modified potentialr2 2____aq ID/ff(r)= 2 — — ——cos0(r). (3.14)2mr 2r rWriting the potential this way assumes that there is no energy transfer between the rotation of the polar molecule and the orbital motion of the system as a whole. (Thus,angular momentum conservation is not obeyed, as the rotational angular momentum ofthe molecule does vary in this approximation.) As before, the conditions aff/ar = 01 In the original derivation of the ADO theory, 0 was calculated, but Su, Su, andBowers [117] later corrected this to give the treatment outlined here. This changeincreased C slightly, increasing the predicted rate constants—an improvement. Thecorrected values of C are used in this thesis.46at b and ff(rC) = E are invoked to give= r + 2rE + cos0(r) (3.15)oru(E) = + + D cos0(r) (3.16)andE= 2q+2q (acos 0) (3.17)mr mr or r=rwhich are still, alas, functions of r. While r cairnot be eliminated from these equationsexplicitly, they can be solved implicitly; the real problem is to calculate cos 0.The starting point is, of course, to write the definition of average in terms of 0 andits probability P(0);f cos OP(0) dO— fP(0)dOSolving this using equilibrium statistical mechanics is not what is needed because it wasassumed that there was no net energy transfer from rotation, so no equilibrium is established. Since the molecule spends less time at an angle where 0 is high and more where0 is low,P(0) o sin 0/0 (3.19)where sin 0 is simply a geometric factor. Substituting the square root of the rotationalkinetic energy for 0, but writing it as the total rotational energy Er0t minus the rotationalpotential givesI cos 0 sin 0 dO / i sin 0 dOcos0= I I I (3.20)Erot + q cos O/r2 / + cos O/r2which must be evaluated for two cases: (1) When Erot < qJ/r2 the motion is oscillatoryand the integrations are from 0 = 0 to t, where c is given by Erot = —(q[LD/r2)cos ,.47(2) For Erot > qt/r2 the motion is rotational and 0 oscillates between a minimum andmaximum value; the integration is from 0 = 0 to ir. Both integrals are tractable. Theaverage angle is an average of the two cases for cos 0, weighted by the fraction of moleculeswith Erot > qftD/r2 as determined from the initial reactant energy distribution, usuallythermal; recall the assumption that no energy is transferred between rotational and orbitalmotion. Both cos 0(r) and öcos 0/ar are substituted into equations (3.16) and (3.17), andthe function a(E) is determined implicitly. Thermal rate constants may then be calculated numerically.So how is this any better than classical trajectory or Monte Carlo calculations ofrate constants for every reaction system? There are simplifying assumptions in ADO tolessen its accuracy, notably its non-conservation of angular momentum, yet it still requires numerical calculations and gives no final “formula.” The answer is that there isa formula: equation (3.13). The ADO theory has been used to calculate values for the0.300.250.20C0.150.100.050.000.0 0.4 0.8 1.2 1.6 2.0,LD/\/a (Debye K3’2)Figure 3.2 A plot of the ADO theory locking constant C vs. zD/\/ at 300 K; takenfrom reference 117.I I48locking constant C which depend only on T and‘D/\/• Figure 3.2 shows values of Cat 300 K. Experimenters can then read a value of C from such published curves [116,117]to calculate rate constants for their reactions. This simple parameterization is probablythe salient reason for the ADO treatment’s wide appeal.In the years since its introduction, there have been refinements to the ADO treatment,notably the AADO theory [117] in which angular momentum transfer between rotationand translation is treated approximately. In the AADO treatment the orbital angularmomentum is writtenL(r) = mvb— CL, (3.21)whereCL = Ps — = — (3.22)for a system with moment of inertia I, making the effective potential= (mvb— CL)2——cos 0(r). (3.23)2mr 2r rThe two equations expressing g vs. E are more complex than before:a(E) = = [(r + + cos 0(rc)) + (3.24)E=(B+/B2_4D) (3.25)whereB2q1 (acos 0) — 2oq 1rnr arr mr m ar r=randD —oq2 faq2 2[Lq (acosON (‘ÔC 2— m2r r — r 8r ) r — m or ) rq[L I (OcosON 2 2 (OCLN 2+m2r1qfLor ) r — — cos0(r) \Or) rr49When cos 0 is evaluated as for ADO, these equations can be parameterized to give thesimple equationkAAD0=(+ CD2/kT + (3.26)which is valid for very small molecules (I < i0 g cm2), and where Z is a parameterwhich depends (inversely) on temperature alone (Z = 8.63 x 10_18 s cm” g’ at 300 K).A parameterization for larger molecules at 300 K is also given as________37 2 1/2kAADo=-{v+ CD\/2/7rkT + i74} (3.27)where1.39F = + 0.375,a x 1024 + 2.74and a is in cm3, uD is in Debye, and I is in g cm2.In the AADO theory, strict energy conservation is abandoned in favor of angularmomentum conservation. Is it an improvement? According to data [117] presented by itsdevelopers it is, raising the predicted rate constants by 10—20% over ADO, to agree muchbetter with experiment. Perhaps more importantly, AADO agrees better with classicaltrajectory calculations [118—120] than does ADO. This comparison is shown in figure 3.3which shows the predictions of various classical theories over a wide range of reducedtemperature, defined as = 2akT/p, to be explained in the next section.A further development in the ADO lineage is the AQO theory [108] which incorporatesthe charge—quadrupole attraction. It is developed much like the AADO theory but withthe modified potentialV(r) =—cosO— (1 —3(cos0)2) (3.28)where /LQ is the quadrupole moment of the molecule. According to the AQO theory, rateconstants are not affected much by the quadrupole moment; and measurements on molecules with substantial quadrupole moments have shown no influence at all [57]. Bates haskkL5.4.3.2.1.502. 3. 4. 5. 6. 7.Figure 3.3 Plot of k/kL vs. l/J7 = 1tD/V’2okT for various classical theories ofion—molecule capture: a) locked dipole [115]; b) Barker and Ridge average energy treatment [119]; c) variational transition state theory [120]; d) parameterized trajectorycalculations [118], dashed for legibility; e) AADO theory [117]; f) ADO theory [116,117];g) Langevin rate, ignoring the dipole [110]. The VTST and AADO lines come closest tothe trajectory calculations, with AADO being best, but other theories have distinct shortcomings. Note that all except the VTST theory approach the Langevin result in the limitof high TR.6.0.0. 1.51also worked on versions of the ADO theory [121], proposing alternate averaging proceduresthat still conserve angular momentum. Furthermore, he prefers that the factor cos 0 beapplied to the force rather than the energy.It was stated without justification above that a thermal average of cos 0 was inappropriate for examining ion—dipole collisions. The justification is the same as used forintroducing the AADO theory: as a dipole approaches an ion, orbital angular momentum(thus, energy) is transferred to the dipole’s rotation. The rotation of the dipole cannot be characterized by its original temperature; or, indeed, by any temperature, as therotational energy loses its Boltzmann distribution.Nevertheless, such an equilibrium treatment was used by Barker and Ridge [119]who calculated an average interaction energy based on the rotational temperature of thedipole. Their analysis overestimates most ion—dipole reaction rates, but not as badly asthe locked dipole approximation, both shown in figure 3.3. Their method, however, doesagree reasonably well with data for momentum transfer collisions [119,122—124], probablybecause such elastic collisions without capture take place at large separations where therotational temperature of the dipole is relatively unperturbed. Ridge et al. [125,126]modified this treatment to calculate an average free energy for the interaction, and theresults were much more acceptable for ion—dipole capture reactions. In fact, the averagingprocedure was shown [126] to be the same as canonical variational transition state theory.3.4 Transition State TheoryMore in the mainstream of reaction rate theory are the transition state treatments ofion—molecule reactivity. These include both canonical and microcanonical analyses forpolar and non-polar molecules. Transition state theory (TST) does assume an equilibriumbetween degrees of freedom of the system, although the use of microcanonical TST allowsfor non-thermal distributions.52An opportune starting point is the rederivation of the Langevin capture rate constantwhich can serve as a model for the more involved ion—dipole derivation. The canonicaltransition state derivation [111] was the original but it is limited to reactants with anequilibrium thermal energy distribution, so what follows is a microcanonical variationalderivation. It is similar to that presented by Chesnavich and Bowers [107] which wasformulated in terms of flux through the surface in phase space dividing reactants fromproducts.The microcanonical rate constant iskEW(E-V)hE (.)where p(E) is the translational density of states at infinite separation; h is Planck’sconstant; and W(E— V) is the number of internal states of the activated complex, notcounting the one degree of freedom corresponding to the reaction coordinate, taken tobe the radial direction. Thus W is evaluated at some fixed r = r. Note that W is afunction of E— V which is the translational energy of the colliding pair, in this case atthe transition state. Classically,p(E) = 27r(2m/h2)3/E1’ (3.30)and W is given by the volume of the phase sub-space at the transition state:W(E — V) = ff 11E-V dp dp d d. (3.31)h E01b=OThis is integrated in appendix A to giveW(E — V) 82rnr (E + aq2/2r4). (3.32)When equations (3.30) and (3.32) are substituted into eq. (3.29) and evaluated at r =the result isWE— 2wr(E + aq2/2r4) (3 3353At this point, r could be assigned according to the Langevin criterion for r, butthat would defeat the purpose of this exercise. Instead, the variational method is used tofind r:= 0=(2rE — cvq2/r3) (3.34)2 1/4r= () (3.35)which, when substituted into eq. (3.33) givesk(E) = 2irq/7which is just kL as given in equation (3.7).The case of ion—dipole capture is complicated by the rotation of the dipole— witha non-central potential the reaction coordinate is no longer simply the radial direction.Recently there has been a suggestion [127] for an iterative version of TST to cope withthe non-spherical dividing surfaces of ion—dipole capture, but there is as yet no completesolution; all other TST treatments assume a spherically symmetric dividing surface. Since,even assuming spherical symmetry, the dividing surface varies with energy, canonical TSTcan only provide an upper bound to a microcanonical treatment, which gives an upperbound to the reaction rate. The method of choice is then the microcanonical variationalTST analysis of Chesnavich, Su, and Bowers [120].If the dividing surface is spherical, the number of states of the activated complexcan be written as a ten-fold integral analogous to equation (3.31), adding three angulardegrees of freedom for rotation of the dil)ole. With some care for angular momentum andenergy conservation, integration over most variables is relatively straightforward as in theLangevin case, but the final integration over 0 must be divided into the same two ranges54as for the ADO calculation: oscillators and rotors. Finally, the variation of r giveskL3/2[882 + 208 — 1 + (88 + 1)3/2], 8 5/9k(E) =kL13/2[2(9912 + 38 + 1)3/2 + (38 + 2)(68 + 1)(38 — 1)11/2, 8 5/9(3.36)whereI = 2aE/.Note that this variational rate constant bundles all the dipole dependence into the reduced energy 8. Thus, the thermal average rate constant depends only on the reducedtemperatureTR = 2akT/. (3.37)Figure 3.3 uses this reduced temperature to compare the various theories. At low reduced temperatures, the VTST treatment agrees well with both AADO and trajectorycalculations, lending confidence to each, but at high temperatures the VTST result goesto kL instead of the true Langevin limit! This failure is caused by the TST assumption that energy is continuously redistributed among all degrees of freedom: in the caseof zero dipole moment or a rapidly spinning dipole there is no mechanism for the (dipole)rotational energy to be transferred to orbital motion.3.5 Trajectory CalculationsThe best way to evaluate the relative merits of these treatments is not really by comparison with experiment because they all make the capture assumption which may notbe borne out for any particular reaction. The usual way to test the approximations ofa theory is to perform simulations incorporating the same assumptions. When classicaldynamics are assumed, it is straightforward to calculate trajectories of the reactants fromany initial state and, assuming simple capture, to determine if they react from that state.55Dugan and Magee [128] were the first to perform numerical ion—dipole trajectorycalculations, reporting capture cross sections for a number of systems, real and fictitious.They calculated random trajectories starting at r = so A separation by numericallyintegrating the Lagrarigian equations of motion, and assumed capture occurred if thereactants approached within 2 A. They found “capture” rates between the Larigevin andlocked-dipole extremes, and relatively insensitive to the moment of inertia of the molecule.Chesnavich et al. [120] also performed trajectory calculations, but integrated theHamiltonian equations of motion with time reversal: the trajectories started at the Lamgevin capture radius for b == (q2/2E)1/4 (3.38)and were terminated when the reactants re-crossed r (non-reactive) or reached r + 16 A(reactive). This method improves efficiency by eliminating from consideration many nonreactive trajectories. Their five sample systems spanned a wide range of TR but all felljust below the VTST results, perhaps suggesting that their kTST is high by (\/7— l)kLat all TR. In addition, they showed that k depends only on the reduced parameters fortemperature TR = 2ckT/ and for moment of inertia 1* = uI/cvqm, although theJ* dependence is small. Continuing this line of research, Su and Chesnavich [118,129]performed a series of trajectory calculations and found k was insensitive to 1* in theregion1* < (0.7 + Ti’) / (2+ 0.6T”2) (3.39)where the rate is given byk(0.4767T”2+ 0.6200, TR 0.25= (T’12 + 0.5090)2 (3.40)L10.526 +0.9754, TR 0.25shown in figure 3.3. Unfortunately, they did not parameterize k in the large region whereit is sensitive to J*, which includes low temperatures, but they did [129] tabulate some56values for some molecules at selected low temperatures, some of which are shown infigure 3.4.3.6 Quantum Mechanical TheoriesAll the methods reviewed so far are classical. They are very accurate at moderate tohigh temperatures because the orbital motion of the colliding bodies as well as rotationalmotion of the dipolar molecule is still relatively unhindered at the capture radius, andso densely quantized—the case of the loose activated complex [130]. Nevertheless, theclassical approximation must break down at some point as the energy or temperature islowered; and much of the interest in ion—molecule reactivity is for very cold interstellarreactions [131].The early treatment of Langevin capture by Vogt and Wannier [112] was, in fact,quantum mechanical. Their analysis gives Langevin capture except when the de Broguewavelength of the particle approaches or exceeds the classical capture radius. This isnot relevant for chemistry except for capture of bare electrons—the raison d’être for thatpaper.A complete quantum description of ion—dipole capture is made much more difficult by the same circumstance that makes classical treatments so useful: there are somany rovibrational states to consider. Even at temperatures around 10 K, where a quantum treatment is necessary, there are too may states available for a complete solution;however, there have been approximate treatments proposed recently by Troe [132,133],Sakimoto and Takayanagi [124,134—136], and Clary [137—139]. It may not be apparentat first that a QM treatment is necessary at any temperature because the translationalenergy increases markedly as the reactants approach capture. The important quantization, however, is of the initial reactants; each initial state leads to a separate reaction“channel.”57The approach used by Troe is called the statistical adiabatic channel model, SACM,which was originally applied to unimolecular processes by Quack and Troe [140]. Theadiabatic approximation implies that each initial reactant state can be identified withan individual adiabatic potential energy curve describing the smooth evolution of thatstate from reactant to product. Furthermore, motions are separable, implying that thereaction coordinate is purely radial. The maximum of each channel potential curve givesa channel threshold energy E0 which is used to calculate the activated complex partitionfunction= exp(E0/kT), (3.41)where i enumerates each combination of the orbital quantum number 1, the quantum number for molecular rotation j, and its projection m3 on the i direction. Then canonicaltransition state theory can be used to calculate the rate constant.Unfortunately, the adiabatic potential curves are still too difficult to evaluate exactly.In the original treatment [132], the threshold energies were given by an interpolation between free and hindered rotor potentials; but they were later [133] approximated both byperturbation theory and by two terms of an expansion in r to give the thresholdsBG2F>0= 2 [F(j, m) + cB/t]— (3.42)Ba2 BbF<0whereG = h21(1 + 1)/2mqu,F-3m-j(j+1)j(j+1)(2j-l)(2j+3)’a = 2j—mI + 1,b=m+2inIj—2j —2j—2,58and where B is the rotational constant of the molecule. The sum over i in eq. (3.41) isreplaced by an integral over G (making this treatment semiclassical) which is parameterized to agree with the extreme cases of T — 0 and T — -_ (where it can be integratedanalytically) and with numerically integrated values between, giving the state-resolvedrate constantsm3,T)+ exp (_a413y213) } (3.43)1 (1 + 1.5IX1—expfor F(j,rn) 0, andk(j,m,T) {Y+exP(_a413Y213)}(3.44)x exp (- [a2 - j(j + 1)] ) /(i +a2B/2kT)for F(j,m) <0; where= KkT[y_2 + F(j,m)]/2BandY =These state-resolved rate constants can be averaged to get a thermal average rate.The equations given above are for the case of a linear dipole with isotropic polarizability, although they are not very accurate unless the dipole dominates over the polarizability.Troe [1331 also applied SACM to non-linear dipoles, quadrupoles, and anisotropic polarizabilities. He found that anisotropy of the polarizability should reduce rate constantsbelow kL.The integration over G above suggests a different approach: treat the translationalmotion classically but use a full quantum treatment for the rotation/vibration. This is59the method chosen by Sakimoto and Takayanagi for their perturbed rotational state (PRs)analysis [124,134,135]. They constructed adiabatic potential curves Ujm. and perturbedrotational states Xjm, (0, q, x) which are the solutions toHXjmj (0, , x) Ujm (2)Xjm, (0, ç, x), (3.45)H = 2 +cos0 (3.46)where 0 and q give the orientation of the dipole relative to the i direction (a rotating reference frame), j is the angular momentum operator, and x is a reduced distancex = r/j[LDq. Since V —* 0 as r —* , in the same limit Xjm3(0, x),‘ mj(0 q!), thespherical harmonic free-rotor eigen-function, and Ujm —* j(j + 1). These limits definej and m3 as the quantum numbers for, respectively, the magnitude and projection ofthe molecule’s rotational angular momentum.The relative motion is treated classically, appealing to energy and angular momentum conservation, though the coordinates must be changed to a non-rotating frame toapply the latter. The angular velocity of the rotating frame is = hw/B in reduced units.The time-dependent rotational wave function ib(r) is determined by the time-dependentSchrödinger equation= Hb(r), (3.47)using the reduced time r = Bt/h. i/J is expanded in the PRS basis functions:(r) = Glmi(T) x(° ,x(r)) exp [_ f {u7(x(r)) — m } dr] (3.48)3 m3and solved. Far fewer states are needed for accuracy using this expansion than for anexpansion in unperturbed rotational states.One drawback of this solution is that total angular momentum is not conserved innon-adiabatic transitions between PRS’s because the rotational and orbital motions are60treated by different mechanics. The effect of this is minimal, though, because the rotational angular momentum is much less than the orbital for the low j values considered.Results for initial rotational states j = 0 and 1 agree well with the SACM results [133].Another difficulty is that the coupled solution becomes impractical at higher j values.One fix is to allow transitions only between states of the same j, which was used [124] fordistant momentum transfer collisions. This may be less accurate for capture collisions,but the classical ADO treatment gives no coupling at all.A different approach is to treat even the rotation semiclassically when j is high.Sakimoto [136] used the adiabatic invariant [121,142]+ jp9 dO/ir (3.49)to characterize classical adiabatic channels, where p is given in= B(p +p/(sinO)2)+ ii cosO/r2. (3.50)The rotation is then quantized by applying the Bohr—Sommerfeld quantization rule to n,giving channel curves that are close to the quantum PRS curves. The channel selectedcross sections are calculated from the potential curves just as for classical Langevin capture. Morgan and Bates [141] have provided a parameterization for this semiclassical“adiabatic invariant method” which reproduces the full PRS calculations very well. Thisparameterization is used for the PRS curve of figure 3.4.Clary’s treatment [137,138] is quite similar in that it is also an adiabatic channelmodel, but it uses the centrifugal sudden approximation for non-reactive scattering toevaluate the adiabatic channel potential curves. Thus the method is called ACCSA, foradiabatic capture—centrifugal sudden approximation. The CSA assumes there is no coupling between different M-states (where M is the projection of the system’s total angularmomentum J). As long as only M-averaged rate constants are reported, this approximation should be reasonable, even for the long range ion—molecule interaction. To reduce the6100 10 20 301//TRFigure 3.4 Comparison of the SACM, parameterized PRS, and ACCSA quantum mechanical treatments of H + HCN association at low temperatures, along with classicaltrajectory (CT,.), ADO, and AADO calculations. The CT and ACCSA results agree verywell even below 10 K, perhaps fortuitously, while PRS and SACM agree on much lowervalues of k. The PRS parameterization of Morgan and Bates [141] is only for j 2 so itis limited to low temperatures. Conversely, the ADO and AADO results are only shownabove T = 50 K, which is already too cold for them.T(K)1253014 8 570605040302010kkL40 50 6062number of states to consider, the molecular rotation is expressed in a “localized rotationalbasis” weighted for 0 = 0, the energetically favored orientation. Capture is defined bysetting a reaction probability to 1 for lower J values and to 0 for J > Jmax, where Jgives the highest angular momentum for which the centrifugal barrier can be crossed.The J-resolved cross sections are evaluated by summing up to 1maxFigure 3.4 shows a comparison of the low temperature ACCSA, PRS, and SACM predictions for H + HCN, along with some low temperature classical trajectory calculations [1291. The ACCSA calculation agrees well with the trajectory calculation, but thatis of dubious merit. The agreement between ACCSA and SACM is much worse, especiallyat the lowest temperatures. Although Troe’s SACM treatment involves many approximations, they do not affect the T— 0 limit, which should, then, be accurate. The SACMcurve agrees well with the PRS calculation (as well as a more recent AC treatment [143]by Markovié and Nordholm). For these reasons, and for the ease of calculation, the SACMtreatment is the method of choice for low temperature results in this thesis.Chapter 4RESULTS AND KINETIC MODELSWhen muons are stopped in helium or neon, no muonium is observed owing to boththe high ionization potentials of these gases relative to Mu and the magnitude of theepithermal charge exchange cross sections involved [44,85]. At pressures around 1 atm orhigher, essentially all the muon polarization is retained in some diamagnetic species andis manifest as a long-lived large-amplitude precession at the diamagnetic (or bare muon)Larmor frequency. Sample spectra are shown in figure 4.1 (for He) and back in figure 1.4(Ne). Positive identification of the diamagnetic species involved is part of the rationalefor this thesis, but a tentative identification as the muonated molecular ions HeMu+ andNeMu can be made following a previous study [44]. For now, suffice it to say that themolecular ion is the only reasonable possibility.The signal changes dramatically upon the addition of even 10 ppm of easily ionizable gas, as illustrated in figure 4.2 for 6.8 x iü’ moleccm3of NH3 added to 2280 torr(8.06 x 1019 moleccirf3)of He. The diamagnetic signal clearly shows a two-componentrelaxation described by ADG(t) = A1 exp(—)t) + A2 exp(—Xt), i.e., equation (1.15).In the case of figure 4.2‘2 = 2.3, = 0.04 [ts, A2 = 0.074, and A1 = 0.243. Results ofthis nature are tabulated in Appendix B for a wide variety of reagent gases in helium andneon moderators, with a few results obtained in argon and nitrogen moderators also. Allbut a few cases exhibit the characteristic diamagnetic relaxation. Also tabulated are the63I.>‘ci)EE>.‘(I,640.350.251.0 2.0 3.0 4.0 5.0 6.0 7.00.05—0.05—0.15—0.25—0.350.0Time / ,usFigure 4.1 The 300 G 1tSR signal A(t) for 2280 torr helium showing a large, long-lived diamagnetic signal, attributed to the molecular ion HeMu+. The slow relaxation(.) = 0.02 its’) is consistent with the magnetic field inhomogeneity.0.350.25—0.15—0.25—0.350.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Time / 1usFigure 4.2 The relaxing signal seen in 2280 torr He with 6.8 x iO’4 moleccm3 ofadded NH3 (8 ppm). The curve is a fit of equations (1.10) and (1.15) to the data. Therelaxation is attributed to Mu formation by dissociative charge exchange between HeMu+and NH3.65results from investigations of temperature and pressure dependerices, and of mixtures ofreagent gases.This chapter progresses through three stages. In the first, relaxation data are presented and the minimal reaction mechanism to account for that data is found, and used forthe data analysis. In the second stage (4.5—4.8) a complete reaction model is presented,and the effects of its various reaction channels and limiting cases are considered. Finally,other data are presented whose analysis and interpretation are independent of the mainreaction mechanism.4.1 Measured Relaxations and AmplitudesAs indicated by figure 4.2, or by a more laborious inspection of appendix B, the twocomponents have very different’ relaxation rates, which may be called the “fast” and“slow” components. The parameters of interest are then Af, A, \f, and ). In general,did not vary much; its interpretation is deferred and the slow-relaxing component istreated as non-relaxing. Conversely, .\f varied with reagent and moderator gas, and isthe most important parameter measured.The amplitudes of the components varied as well, and this variation can provide useful information. In order to get a meaningful amplitude for the slow component though,the contribution made by muons that stopped in the metal walls of the target vessel hadto be subtracted. This correction was determined for each run period (or beam tune)and moderator density by adding 02, air, or Xe to the moderator. It is known that02 depolarizes Mu by spin exchange with a rate of 4 x cm3 molec’ s at roomtemperature [44,106], and no signal at all is seen in inert gas containing more than a‘ One could claim that they are “very” different due to numerical considerationsalone—if the rates were similar, they could not be separated by a fit, and wouldprobably never have been noticed; however, the rates can always be made verydifferent by adding more reagent gas.66few torr of 02. Xe produces 100% Mu and no diamagnetic fraction at pressures below25 atm [91]. Thus, the amplitudes measured in these mixtures directly give the contribution from muons in the target walls. The amplitudes of these ‘wall signals’ were generallysmall (sometimes vanishingly small) thanks mainly to the very large target vessel andvariable-momentum beamlines. The amplitudes listed in appendix B have already hadthe wall contributions subtracted.4.2 Relaxation MechanismThe relaxation of the diamagnetic signal is interpreted as due to muonium formationby charge transfer between the reagent gas ‘X’ and the muonated rare gas ion MMu+(M = He, Ne,.. .). The prototype for charge transfer isW++X—*W+X+ (4.1)but since W = MMu is not bound (figure 1.1), the ion undergoes dissociative chargetransfer according toMMu + X Mu + M + X. (4.2)The fast-precessing Mu rapidly (in effect, instantaneously) loses phase coherence withthe rest of the muons, giving relaxation of the signal at the chemical reaction rate aspreviewed in section 1.7.A slight modification to this process is the switching reactionMMu+X—*Mu+MX (4.3)which is energetically more favorable, though entropically less so. It could be important when reaction (4.2) is endothermic and there is not quite enough excitation energyavailable to make it go. The binding energies of all HeX and NeX are so small (BE ofXeNe = 4.1 kJ/mol 0.042 eV [144]) that such switching reactions should be of littleconsequence in these studies.67The only other possibility for the relaxation is the formation of a different paramagnetic product by muon transfer, say byHeMu + NO A NOMu + He. (4.4)Of the reactants studied, this should only occur for X = NO and 02 forming the radicalions NOMu and O2Mu. At 300 G, the spin in these radicals, even with their reduced(from Mu) hyperfine couplings, would still lose phase coherence with the diamagnetic ensemble very rapidly. For these two cases it is possible that the apparent ke is actually thesum k + ke. Alternatively, fragmentation of diamagnetic products, e.g.NeMu + CH3NO2A (CH3NO2MuI* •, CH3Mu + NO2 (4.5)could produce pararnagnetic ions, but fragmentation is much more likely to produce otherdiamagnetic species, e.g.NeMu + CH3NO2—* Ne + (CH3NO2Muj*‘V { CHE+MuNO2 (4.6)HeMu+ C2H4 —* He+ (C2H4Muj* —* CH2Mu+ H2. (4.7)Radical formation, both directly and by fragmentation, is considered further later, but itdoes not affect the fits to the data presented here.For all of reactions (4.2)—(4.4) one expects a linear dependence of the relaxation rateon reagent concentration [X]. Such is indeed the case for the reactions investigated;some results of linear fits to the relaxation data are shown in figures 4.3 and 4.4, andthe experimental rate constants (slope, kexp) are listed in table 4.1. These fits use themodified regression method outlined in section 2.3 incorporating both the statistical uncertainties in relaxation rates \ and concentrations [X]. The error bars shown are lo, asare the reported uncertainties in k. (For clarity, the plots show the weighted average )for each run, but individual values of \ from each histogram were used for the fits.) The688.07.06.05.04.03.02.01.00.0NeMu + NH3 (0), C2H4 (•), NO (h), 02 (.), Kr (o)Figure 4.3 Linear fits of vs. concentration for a number of reactants in neon, wherethe slopes give the experimental rate constants 1exp = 26 (NH3,o), 19 (C2H4,.), 9.2 (NO,), 6.4 (02,.), and 0.6 (Kr,D) x 10’°cm3mole ’s’ for for the total reaction rate withNeMu+, at neon moderator pressures from 800 to 1300 torr, and at room temperature.3.01.50.0HeMu + CH3NO2 (s), TMS (•), N20 (o), NO (.)0 5 10 15 20 25 30 35 4014—3[X] (10 molec cm )Figure 4.4 Reaction rates of HeMu+ with various neutrals, plotted with linearfits which give k6 58 (CH3N02,z), 31 (TMS = (CH3)4Si,.), 20 (N20,o), and14.7 x 10’° cm3molec’ s (NO,., which has another point off the graph). All pointswere measured at room temperature and at 2280 torr of He, except for the N20 runswhich were taken at 1500 torr pressure.U)..—O 10 20 30 40 50 60 7014 —3[X] (10 molec cm )80 90 1009.07.56.04.5Cl)1<69random uncertainties in [X} were estimated from the nominal accuracy (0.5%) and theobserved variability of the pressure measurements (when filling the standard volume withreagent gas). In some cases, an additional, systematic, uncertainty was added to therate constant to reflect uncertainty in the ‘standard’ volume. In almost all cases, theuncertainty in [X] was of much less consequence than the uncertainty in ). Occasionally,as well, the uncertainty reported for kexp was increased somewhat arbitrarily because ofexcessive scatter in the points (high x2).The rate constants do vary somewhat in their uncertainties: 3% 40%, with a typical error bar of 15%. These compare favorably with more established ion—moleculekinetics measurements [26]. There are several repetitions in table 4.1 that reveal the levelof reproducibility. This is usually good, but two stand out and deserve special mention:Methyl fluoride reacts with NeMu twice as fast at 800 torr as at 1400 torr. The measurements were done consecutively which suggests this is a real effect involving quenchingby the moderator (see later). These runs were done without cold-trapping the neonthough, suggesting that the different kexp’S and the high intercepts are due to some impurity in the neon. This scenario is inconsistent, though, because of the reverse dependenceon pressure. The high value of 12.26 at 800 torr is closer to the measurements made atdifferent temperatures.Nitric oxide in 800 torr argon gave very different rate constants and amplitudes fortwo separate determinations. Based partly on prejudice, the measurement with the lowerrate and higher amplitude seems right. The high relaxation may have been due to animpurity, either from the NO bottle or from leaks; the latter would cast some doubt onmeasurements taken in the same run period [(C2H5)3N and the 400 torr NO in Ar, andsome ternary mixtures, given below]. Alternatively, the inconsistency may be the resultof the reduced diamagnetic signal in Ar as compared with He or Ne.It is worth emphasizing that these cases are exceptional, in that most repeatedmeasurements of kexp agreed within their uncertainties.70Table 4.1 Experimental Rate Constants Determined by FittingReactant M a b T C k d Intercept kexp qKr Ne 1000 0.50 + 0.16 0.57 + 0.18 17.5 + 5.5Kr Ne 800 0.62 ± 0.15 0.243 ± 0.089 9.3 ± 3.4Xe Ne 1300 3.0 + 0.3 0.82 + 0.15 19.3 + 3.5Xe Ne 1300 3.6 ± 1.3 1.46 ± 0.22 34.3 ± 5.2Xe Ne 1000 5.4 ± 2.8 0.51 ± 0.13 15.4 ± 4.0Xe g Ne 800 5.35 ± 0.28 0.317 ± 0.034 12.1 ± 1.3Xe Ne 1400 445 4.93 ± 0.32 0.55 ± 0.10 18.2 ± 3.2Xe Ne 565 179 5.30 + 0.38w 0.136 + 0.087 4.5 + 2.9Xe Ne 370 117 5.39 + 0.24 0.044 + 0.014 1.44 ± 0.46Xe q Ne 1000 117 4.77 ± 0.40 0.009 ± 0.019 0.11 ± 0.2302 Ne 800 6.43 ± 0.37 0.063 ± 0.034 2.4 ± 1.3NO Ne 800 7.17 + 0.64 0.315 + 0.091 12.0 ± 3.5NO Ne 800 9.17 + 0.39 0.036 ± 0.053 1.4 ± 2.0N20 Ne 1000 11.1 + 1.3 0.61 + 0.17 18.6 ± 5.2N20 Ne 1400 445 14.7 ± 1.3 0.16 + 0.18 5.4 + 5.9N20 Ne -.700 177 12.30 ± 0.82 0.06 + 0.15 1.5 + 3.8NH3 Ne 800 27.7 + 4.8 1.19 + 0.26 45. + 10.NH3 Ne 1300 26.4 + 2.0 0.82 + 0.20 19.2 + 4.7NH3 Ne various 26.6 ± 4.0NH3 Ne 1400 445 22.60 + 0.86 0.149 + 0.053 4.9 + 1.7NH3 Ne 567 179 27.01 ± 0.89 —0.059 + 0.067 —1.9 + 2.2C2H4 Ne 1000 18.6 + 3.5 0.61 ± 0.33 19. ± 10.(CH3)4Si Ne 800 16.2 + 2.4 0.26 ± 0.19 9.9 ± 7.3CH3NO2 Ne 800 41.6 + 4.1 —0.04 + 0.15 —1.5 + 5.7CH3NO2 Ne 1300 406 27.7 ± 3.0 0.27 + 0.15 8.7 + 4.8CH3NO2 Ne 740 223 31.6 ± 6.3 0.12 + 0.47 4. + 15.CF4 Ne 800 6.59 + 0.47 0.37 ± 0.12 14.1 ± 4.6CH3F Ne 1400 6.4 ± 1.4 1.98 + 0.28 43.2 + 6.1CH3F Ne 800 12.3 + 3.3 1.47 ± 0.39 56. ± 15.CH3F Ne 1400 445 15.5 ± 1.2 0.51 + 0.11 16.8 + 3.8CH3F Ne 700 179 11.9 ± 1.2 0.75 + 0.19 19.9 ± 5.0Continued...71Table 4.1 (continued) Experimental Rate Constants Determined by Fitting Af1.60 + 0.330.194 + 0.0390.53 + 0.232.16 ± 0.580.056 ± 0.067—0.10 ± 0.150.39 ± 0.120.63 + 0.140.77 ± 0.110.09 ± 0.260.17± 0.130.68 ± 0.270.09 ± 0.18—0.11 ± 0.122.06 ± 0.720.63 + 0.111.01 ± 0.120.76 ± 0.1332.6 ± 6.72.60 ± 0.5210.8 ± 4.744. ± 12.0.75 ± 0.90—1.7 ± 2.65.2 ± 1.68.4 ± 1.913.5 ± 1.91.7 ± 4.62.3 ± 1.713.8 ± 5.51.6 ± 3.1—1.8 ±2.037. ± 13.11.0 ± 1.916.3 ± 1.914.0 ± 2.4a Moderator gas ‘M’ implies the molecular ion MMu+ i.e., HeMu+, NeMu+, ArMu+, andN2Mu+. Neither H2 nor C2H6 moderators showed any reaction.b Moderator pressure in torr.Temperature (kelvin); blank entries imply room temperature.d The experimental rate constant (slope) in 10_b cm3 molec1s’; kexp can usually beidentified with the capture rate constant k.eThe intercept of ) vs. [X], in identified as the moderator quenching rate kq[M].The quenching rate constant, in 10_15 cm3 molec’ s1, as determined from the intercept.q Relaxation rate did not vary linearly with concentration, as shown in figure 6.6. Thetabulated values are from fitting the low concentration points.Reactant M a b T C k d Intercept e kexp qHeHeHeHeHeHeHeHeHeHeHeHeHeHeHeHeHeHe150022801500150022802400228022802400950228015002400800170024001330830XeNON20NH3NH3C2H4(CH3)4SiCH3NO2CH3HOCH3HOCF4CH3FCH3FCH3FC2H4FC2H4FC2H4FC2H4FNONONO(C2H5)3NNO39840616339812840620814812.9 ± 2.614.68 ± 0.3620.0 + 2.276.9 + 14.234.7 ± 1.425.0 ± 1.831.1 ±2.357.5 ± 4.431.5 ± 2.565.0 ± 7.816.2 ± 1.433.0 ± 4.926.5 + 2.847.7 ± 3.414.0 + 4.99.2 ± 1.018.7 ± 1.636.7 ± 3.33.21 ± 0.166.1 ± 1.66.3 ± 4.28.6 ± 4.01.46 ± 0.14Ar 800Ar 800Ar 400Ar 800N2 8000.018 ± 0.012—0.13 ± 0.47—0.07 ± 0.870.63 ± 0.440.176 ± 0.0750.68—5.—5.24.± 0.45±18.±66.+17.6.7 ± 2.9724.3 A Simplistic ModelDespite the convincing fits to the relaxation rates, reaction (4.2) alone cannot explain theresults because it does not provide for a two-component signal relaxation. The amplitudesof each component are tabulated with the relaxation rates in Appendix B. It can be seenthere that the relative amplitudes of the two components varied greatly with reagent gas,as made clear by figures 4.5 and 4.6 for the extreme cases of nitromethane and nitricoxide. A proper model for these reactions must account for both the relaxation rates andthe amplitudes.The observation of two-component relaxations indicates that there are two groupsof muons in diamagnetic environments. However, rather than being distributed betweenthese groups initially, all the initial diamagnetic signal likely comes from a single muonatedmolecular ion species, and the separation is caused by competing reactions, according toMu-j-X-j-MMMu + X (4.8)k\XMuH-Mwhich was proposed in ref. 27. Here the diamagnetic MMu+ reacts with the dopant, X,by charge (electron) transfer with rate constant ke to give muonium, or by muon transferwith rate constant to form diamagnetic XMu+. Such a muon-transfer reaction is entirely expected, based on the prevalence of the analogous proton-transfer reactions, whichhave been well studied [16,24,25,79,139,145—149]. Since XMu is (usually) diamagnetic,and as no diamagnetic frequency shift is large enough to give measurable dephasing onthe few-microsecond time scale investigated, there is no relaxation associated with themuon-transfer reaction. As mentioned in the previous section, and discussed later, theproducts of muon transfer may fragment, but other diamagnetic products will be theresult. Therefore, the relaxation envelope is given by the total concentration of diamagnetic species over time. As only a few million muons are used per experiment, and only>‘Q)EE>‘LI)-I-.>.‘a)EE>.‘Li)731.0 2.0 3.0 4.0 5.0 6.0 7.00.300.200.100.00—0.10—0.20—0.300.0Time / ,usFigure 4.5 The SR signal AQ) showing the reaction between HeMu and 2.3 xi0’ moleccm3of riitromethane, giving = 2.4 Af = 0.079, and A5 = 0.240. Theslowly relaxing component has been outlined to highlight the small fast-relaxing component. The amplitudes indicate that CH3NO2 reacts predominantly by muon transfer inpreference to charge transfer.0.300.200.100.00—0.10—0.20—0.300.0 1.0 2.0 3.0 4.0 7.0Time / psFigure 4.6 The strongly relaxing signal seen for HeMu+ with 35.5 x 1014 moleccm3ofnitric oxide; )if = 5.1 A = 0.307, and A5 = 0.012. The slow relaxation envelope isdrawn for clarity. The large relaxing component is attributed to efficient charge transfercoupled with inefficient muon transfer, possibly with depolarization of NOMu+ even aftermuon transfer.5.0 6.074one muon at a time is permitted in the target, the X and M species are in vast excess,allowing a straightforward analysis from elementary (pseudo-first order) kinetics.The concentration of the initial ion is[MMu] = [MMu]0e_+jt (49)and the concentration of the other diamagnetic species, XM11+, is[XMu] = k[MMuj0{i — e_+[xht}. (4.10)ke + kThe relaxation function is the normalized sum of these:G(t) = [D]/[D]0= ke+ke +ke_jt (4.11)where MMu is taken to be the only species present at t = 0 so that [DJ0 = [MMuj0.Thus there are two components to the signal: one relaxing at ) = (ke +k1j[X] and theother not relaxing at all. The relaxing component of this model is identified with thefast-relaxing component of the (lata, ..\ = ), and the non-relaxing component correspondsto the observed slowly-relaxing component, and the slow relaxation must be attributedto other processes (e.g., dephasing due to magnetic field inhomogeneity).This model is a big improvement over simple charge transfer, but it is still incomplete.The first, and most serious, shortfall becomes apparent with a consideration of the energetics for charge transfer. Reaction (4.2) is endothermic by the ionization potential (iP)of reactant X plus the binding energy (D0) of the initial ion MMu, minus the IP of Mu(13.533 eV [81]): E = iP(X) +D0(MMuj — 1P(Mu). Table 4.2 lists the endothermicitiesfor most combinations of X and M measured for this thesis; the cases where a reaction wasseen are checked, and combinations where no reaction was evident are indicated by an x.In addition to the combinations tabulated, some investigations of molecular moderatorswere performed, with no relaxation seen for ammonia, triethylamine or nitric oxide inhydrogen; none for ammonia or nitric oxide in ethane; and none for C2H4, CO, or 0275Table 4.2 Dissociative Charge-Transfer Reaction EndothermicitiesaNeutral IP (eV)b IonHeMu NeMu ArMu1.53c 1.79’ 357CKr 1400d 1.99 e 2.25 Ve 4.03Xe 12.13 0.12 V 0.38 V 2.16 x112 1543d 3.42 x 3.67 x 5.46co 1401d 2.01 x 2.26 x 4.0402 12.06 0.05 0.31 V 2.09 XNO 9.26 —2.75 —2.49 —0.71N20 12.89 0.88 1.13 2.92NH3 10.16 —1.85 —1.59 0.19 xH20 12.61 0.60 x 0.86 x 2.64CH4 12.51 0.50 x 0.76 x 2.54C2H6 11.52 —0.49 x —0.23 x 1.55C2114 10.51 —1.50 V —1.24 V 0.54(CH3)4Si 9.80 —2.21 —1.95 V —0.17 x(C2115)3N 7.1 b —4.91 —4.65 —2.87 VCH3NO2 11.02 —0.99 —0.73 1.05CH3N 12.19 0.18 0.44 x 2.22CH3HO 10.23 —1.78 —1.52 0.26CF4 13. b 0.99 1.25 3.03CH3F 12.47 0.46 0.72 2.50C2H4F 11.87 —0.14 0.12 1.90a /E for the reaction MMu+ + X —* X+ + Mu + M, in eV, where X is the neutral specieslisted in the first column. For LE < 0, the reaction is exothermic from the groundstate of the ion.b First ionization potential of the neutral; taken from ref. 144. The value for CF4 (listedthere as “< 14.7”) was here estimated from trends in the fluoro- and chioro-methanes.(Tichy et al. [79] bemoan the fact that the literature value is too high, without mentioning which literature or which value!) The IP for (C2H5)3N, is the median of manyvalues reported [144,150].The ground state binding energies (D0) of the ions [75,78].d Reaction is endothermic even for a bare fhWhether or not any (“fast”) relaxation was observed is indicated by V (yes) or x (no);the absence of a mark indicates that the ion/neutral combination was not examined.76in nitrogen, although nitric oxide did give diamagnetic relaxation in N2. With both themolecular and rare gas moderators, there is no obvious trend with endothermicity, exceptthat no reaction was seen for X = H2 or CO, for which charge transfer is endothermiceven for a bare (Although reaction with Kr is similarly endothermic, a slow reactionwith NeMu+ was observed.) More noteworthy are the cases where the reaction is allowedenergetically, but was not observed (C2H6 in He & Ne; (CH3)4Si in Ar). These caseswill be returned to. Note that these negative results come from multiple trials over wideconcentration ranges to ensure that no relaxation was missed because it was too fastor too slow. Most at odds with the proposed two-reaction mechanism, eq. (4.8), are theinstances where charge transfer is endothermic from the ground state of the molecular ion,but the reaction was seen anyway: 02, N20, CH3F, CF4, and Xe in reacting with HeMu+and NeMu+. These results strongly indicate that the ion is reacting from a rovibrationallyexcited state. Such a refinement was recognized as necessary even when the too-simplemodel (4.8) was originally proposed [27]. This excitation will figure prominently in otherkinetic models to follow shortly and in later discussion.Another failing of mechanism (4.8) is its prediction of the amplitudes. Yes, there aretwo components, but their relative amplitudes are given by A/Af = k,/ke, independentof reagent or moderator concentration; this is surely not the situation revealed by themeasured data. Figure 4.7 illustrates this for a number of cases; clearly, Af grows at theexpense of A as the reagent concentration is increased (note the reciprocal 1/[X] scale),and Af declines as the moderator density is increased. Moreover, figure 4.7 shows thatthe ratio A/Af varies linearly with l/[X] and with [M].The third problem lies with the often substantial intercepts of the vs. [X] fits (seetable 4.1 or figures 4.3 and 4.4). These extrapolations to zero concentration are clearlydifferent from the relaxation rate in pure moderator. This problem was noted, with muchconcern, in ref. 27, but the explanation had not become evident at that early stage ofthis thesis work.a) HeMu + Xec) NeMu + CH3F1.751.501.251.00< 0.750.500.250.00b) HeMu + (CH3)4Sici) NeMu + CH3FFigure 4.7 Four plots showing the variation of relative amplitudes with reactant concentration and moderator pressure (or density). For both (a) Xe in 1500 torr He and(b) (CH34Si in 2300 torr He, the linear dependence on reciprocal concentration is clear,although it is much stronger for Xe. Varying the concentration of CH3F in Ne (c) showssimilar behavior, and varying the Ne pressure (d) reveals a strong linear dependence on p.Plots a, b, & c are fairly typical while plot d shows the strongest pressure dependence measured. Note that plots c&d give different intercepts—see §4.8.775.04.03.02.01.00.00.00 0.10 0.20 0.30 0.401/[Xe] (10 cm3/molec)0.00 0.10 0.20 0.30 0.40 0.501/[TMS] (10 cm/molec)1.801.501.20‘N1 0.900.600.300.000.00 0.04 0.08 0.12 0.16 0.201/[CH3F] (10_14 cm3/molec)3.02.52.01.50.50.01.00 1000 2000Ne pressure (torr)3000784.4 A Successful Simple ModelAll three shortcomings of the previous two-reaction model can be addressed with additionof a third reaction, between the initial molecular ion and the moderator gas to form adiamagnetic product. Since the ion has to be excited, the obvious reaction is collisionalde-excitation or ‘quenching.’ Thus, the simplest model that consistently accounts for thedata is the three-reaction schemeMu+XH-Mke/(MMuj* +xi I4IqlVl L XM11++MMMuwhich was proposed in [28,151]. As before, the excited molecular ion (MMuj* may reactwith reagent X by charge transfer with rate constant ke to form Mu and be depolarized,or by muon transfer at to form the more stable diamagnetic ion XM11+; or it may bequenched by collisions with the moderator with rate constant kq, after which the dissociative charge transfer channel is closed. In contrast, based on their proton affinities [22,144],muon transfer is expected to be exothermic for every X studied, even from the molecularion ground state. While the de-excited MMu+ may indeed react by muon transfer with Xto form XMu+, that reaction is not shown because, since both ions are diamagnetic, ithas no observable effect on the [tSR signal. For simplicity, the quenching is assumed tobe achieved in a single step.Treating each channel as an elementary reaction, the depletion rate of (MMuj* is= (ke + k)[X] + kq[M] (4.13)and[(MM11+)*} = [(MMuj*]0et. (4.14)Likewise, the concentration of Mu formed over time isk [Xl F(MMui*lrM 1 — el I L I Jo —?t 415—(ke + k)[X] + kq[Mj — e79Since Mu is the only source of depolarization, the relaxation shape is[D] [(MMu+)*] — [Mu]G(t)== [(MMuj*]0— k[X1 + kq[Mj+ke[X1 (4 16)— (ke + k,j[X] + kq[M} (ke + k)[X] + kq[M]which, like the previous model, predicts a linear dependence of the relaxation rate onconcentration ( = = (ke + k)[X] + kq[M]) with slope kexp = ke + k, where theadditional term kq[M} (the intercept) accounts for quenching of the initial excited state.Quenching rate constants determined this way are listed in table 4.1. Furthermore, andin contrast with the previous model, the amplitudes of the two components are related by— k1jX] + kq[M] —+kq[M] (4 17)Af— ke[X1 — ke ke[X]so that AS/Af should vary linearly with [M] and with 1/[X]. Such is indeed the case, asshown in figure 4.7. Equation (4.17) was used to fit A/Af vs. 1/[X] to give the results intable 4.3, which lists the intercepts (k,/ke), slopes (kq[M]/ke), and values of kq determinedfrom the slopes. In general, the amplitudes were not as well determined as the relaxationrates, and the reproducibility (especially in the slope) of repeated measurements suffered,notably for Kr, Xe+NeMu and NO+ArMu. The NO in Ar problem has been mentionedin regards to the relaxation rate. (Note that CH3F in Ne is more acceptable here, giventhe general level of reproducibility). The Xe results show how the amplitudes are lessreproducible than the relaxation rates are—compare the slopes in table 4.3 with kexp intable 4.1.In table 4.3 the slopes are interpreted as kq[M]/ke and the intercepts as k/ke, following eq. (4.17). Thus k, and ke can be determined individually by combining data from therelaxation rates (kexp = k,+ke, from table 4.1) and the amplitudes (As/Af[x] =according to the identities ke = ( + ke)/(1 + k/ke) and k, = (k + ke)/(1 + ke/kp).Values for k and ke are given in table 4.4. A possible exception to this interpretation80Table 4.3 Results of Linear Fits of Relative Amplitudes: A/Af vs. 1/[XJReactant Moder.a Tb Slopec Interceptc kqd(‘X’) (‘M’) (torr) ( K) (kq[M]/ke) (k,jjk; kD/ke)Kr Ne 1000 14. + 23. 2.15 ± 0.29 0.7 ± 1.1Kr Ne 800 —20.9 ± 5.7 1.32 + 0.14 —2.13 ± 0.79Xe Ne 1000 6.37 + 0.86 —0.12 ± 0.20 11.8 ± 6.9Xe Ne 1300 19.77 + 1.49 —0.0085 ± 0.086 17.0 ± 6.3Xe Ne 800 1.98 + 0.14 —0.022 ± 0.009 4.13 + 0.37Xe Ne 1400 445 4.3 + 1.1 0.210 ± 0.062 1.1 + 1.1Xe Ne 565 179 —3.80 + 0.60 0.397 ± 0.027 —4.72 ± 0.82Xe Ne 370 117 0.2 + 1.7 0.016 ± 0.086 0.3 ± 3.0Xe Ne 1000 117 0.01 + 0.44 0.090 ± 0.040 0.00 ± 0.2302 Ne 800 0.93 ± 0.24 0.022 + 0.016 2.23 ± 0.59NO Ne 800 2.47 + 0.65 —0.081 + 0.037 7.4 + 2.1NO Ne 800 1.00 ± 0.32 0.0122 + 0.0090 3.5 ± 1.1N20 Ne 1000 10.8 + 1.1 0.721 ± 0.068 21.3 ± 3.4N20 Ne 1400 445 8.9 ± 1.6 1.085 + 0.094 20.7 + 4.2N20 Ne —700 177 4.51 + 0.91 1.103 ± 0.042 6.9 + 1.5NH3 Ne 1300 1.29 + 0.50 0.377 ± 0.050 5.8 + 2.3NH3 Ne 800 —0.52 ± 1.2 1.36 + 0.26 —2.3 ± 5.4NH3 Ne 1400 445 1.607 ± 0.075 0.343 ± 0.011 8.90 ± 0.54NH3 Ne 567 179 0.39 + 0.21 0.410 + 0.014 2.4 + 1.3C2H4 Ne 1000 11.2 + 1.6 1.28 + 0.16 27.9 + 6.9(CH3)4Si Ne 800 2.23 + 0.61 0.688 + 0.070 8.2 + 2.6CH3NO2 Ne 800 3.06 + 0.45 1.17 ± 0.10 22.4 + 4.1CH3NO2 Ne 1300 406 1.99 + 0.66 1.42 + 0.12 7.3 ± 2.6CH3NO2 Ne 740 223 1.13 + 0.89 1.34 + 0.12 4.8 ± 3.9CF4 Ne 800 4.12 + 0.94 0.390 + 0.031 7.5 ± 1.8CH3F Ne 1400 10.99 ± 1.04 0.765 ± 0.063 8.7 + 2.1CH3F Ne 800 7.43 + 0.77 0.348 ± 0.064 25.8 + 7.5CH3F Ne 1400 445 3.76 + 0.47 1.77 + 0.13 6.9 + 1.1CH3F Ne 700 179 1.54 + 0.40 1.060 + 0.035 2.35 + 0.66Continued...81NONONO(C2H5)3NAr 800Ar 800Ar 400Ar 800—0.115 + 0.0519.58 ± 3.610.4±9.316.5 +4.30.027 + 0.0110.21 + 0.120.71 + 0.390.90 ± 0.36—0.137 + 0.06118.3 + 8.71.+26.28. ± 16.Table 4.3 (continued) Results of Linear Fits of Relative Amplitudes: A/A vs. 1/[X]Reactant Moder.a p Tb Slopec Interceptc kqd(‘X’) (‘M’) (torr) (K) (kq[M]/ke) (kjke; kD/ke)Xe He 1500 10.69 + 0.98 0.354 + .074 20.7 ± 4.7NO He 2280 1.98 + 0.12 —0.004 + 0.005 3.91 + 0.26N2O He 1500 5.20 + 0.70 0.936 + 0.064 10.9 ± 1.9NH3 He 1500 2.97 + 0.46 0.49 ± 0.13 31.2 ± 8.0NH3 He 2280 0.91 + 0.15 0.144 + 0.022 3.70 + 0.63C2H4 He 2400 398 0.46 + 0.33 0.751 ± 0.040 1.13 ± 0.81(CH3)4Si He 2280 1.93 + 0.22 0.573 ± 0.036 5.11 ± 0.70CH3NO2 He 2280 2.68 + 0.22 1.28 ± 0.15 9.1 ± 1.2CH3HO He 2400 406 0.20 + 0.13 0.905 ± 0.034 0.59 ± 0.37CH3HO He 950 163 0.57 ± 0.21 1.041 + 0.059 3.2 ± 1.3CF4 He 2280 8.8 + 1.5 1.28 + 0.12 8.4 + 1.7CH3F He 1500 6.86 + 0.77 1.35 + 0.17 19.6 + 3.9CH3F He 2400 398 3.4 + 1.3 2.29 + 0.18 4.7 + 1.9CH3F He 800 128 1.08 + 0.31 1.436 + 0.074 3.5 + 1.0C2H4F He 2400 406 —0.95 + 0.35 0.749 + 0.034 —0.87 + 0.34C2H4F He 1330 208 2.18 + 0.23 0.793 ± 0.031 3.68 ± 0.50C2H4F He 830 148 1.46 ± 0.17 0.618 + 0.055 6.11 + 0.92a Moderator gas ‘M’ implies the molecular ion MM11+, reacting with reagent ‘X’.b Temperature (kelvin); blank entries mean room temperature.Slope is in i0 moleccm3,intercept is dimensionless. Their interpretation as kq[M]/keand k,jke follows from equation (4.17), although eq. (4.24) gives a more refined interpretation as kD/ke + kd + ks[M1)/ke.ci kq, in 10_15 cm3 molec’ s1, as calculated from kq = (slope X kexp) / {[M] (1 +intercept) }.82of the amplitudes occurs when the muon-transfer product XMu+ is itself paramagnetic,as is the case for X = 02 [152] and NO. Figures 1.6 and 4.6 show that nitric oxide giveslittle, if any, slow-relaxation component, which may be a result of NOMu+ depolarization.Nevertheless, it is still reasonable to use equation (4.16), as long as it is remembered that“k6” may really be the total ke + k. Note that if the muon-transfer reaction causesdepolarization, the reaction from the molecular ion ground state should not be ignored;indeed, the quenching channel should have little effect. In that case, the intercepts of the)f fits (near zero for both NO and 02) should not be interpreted as kq[MJ. There aredifficulties though, notably in explaining the presence of some non-relaxing signal, andthese are discussed later.Another impediment to interpreting the intercepts of the ) fits as kq[M] is their greatvariability; consistent values should be obtained for the same moderator gas (He or Ne)at the same density (pressure), independent of the X reagent. The tabulated results shownot only great variations between different neutrals, but often large differences betweenthe kq determined from the relaxation rates and the value derived from the amplitudes.Inflated and varying ‘quenching’ rates are probably due to reactions of impurities,such as water vapor, in the gas. If the impurity causes no depolarization (as is true forH20; table 4.2) its presence is not obvious, but the muon-transfer reaction, e.g.,NeMu + H20 — Ne +H20Mu (4.18)would give a non-zero intercept to )f. The magnitude of the problem is made clear by thehigh intercepts typical before routine cold-trapping of the moderator gas was instituted(in recognition of this problem). Even when starting with clean gas, though, water vaporcould still be present as it was continuously emitted by the aluminum reaction vessel, evenafter (ineffective) “baking.” Nevertheless, the intercepts of the fits show reasonableconsistency for later runs, and are still interpreted as kq[M]; with discussion in chapter 6.83Table 4.4Experimental MuonRate ConstantsTransfer and Charge Transfer Rate Constants with Total (Capture)Reactant Moder. p (torr) T (K)’ kb ke (kD)Kr Ne 1000 0.56 + 0.11 0.226 ± 0.050 0.334 ± 0.069Xe Ne 800d 5.35 + 0.28 5.47 ± 0.29 —0.120 ± 0.051Xe Ne 1400 445 4.93 ± 0.32 3.31 + 0.34 1.62 ± 0.29Xe Ne 565 179 5.30 ± 0.38 3.79 + 0.28 1.51 ± 0.13Xe Ne C 117 5.22 ± 0.24 4.85 + 0.28 0.37 ± 0.1602 Ne 800 6.43 ± 0.37 6.29 + 0.38 0.14 ± 0.10NO Ne 800c 8.63 ± 0.67 8.57 + 0.68 0.06 ± 0.14N20 Ne 1000 11.1 + 1.3 6.45 + 0.80 4.65 + 0.60N20 Ne 1400 445 14.7 + 1.3 7.05 + 0.70 7.65 + 0.75N20 Ne —700 177 12.30 + 0.82 5.85 + 0.41 6.45 ± 0.45NH3 Ne l300 26.6 + 1.7c 19.3 + 14d 7.28 ± 084dNH3 Ne 1400 445 22.60 + 0.86 16.83 + 0.65 5.77 + 0.26NH3 Ne 567 179 27.01 ± 0.89 19.16 + 0.66 7.85 ± 0.32C2H4 Ne 1000 18.6 + 3.5 8.2 ± 1.6 10.4 + 2.0(CH3)4Si Ne 800 16.2 + 2.4 9.6 + 1.5 6.6 + 1.1CH3NO2 Ne 800 41.6 ± 4.1 19.2 + 2.1 22.4 ± 2.4CH3NO2 Ne 1300 406 27.7 + 3.0 11.4 ± 1.4 16.3 ± 1.8CH3NO2 Ne 740 223 31.6 + 6.3 13.5 + 2.8 18.1 + 3.7CF4 Ne 800 6.59 + 0.47 4.74 + 0.35 1.85 ± 0.17CH3F Ne 800d 12.3 + 3.3 9.1 ± 2.5 3.2 ± 1.0CH3F Ne 1400 445 15.5 + 1.2 5.58 + 0.51 9.88 + 0.81CH3F Ne 700 179 11.9 + 1.2 5.78 ± 0.59 6.12 ± 0.63Continued...84Table 4.4 (continued)Experimental Muon Transfer and Charge Transfer Rate Constants with Total (Capture)Rate ConstantsReactant Moder. p (torr) T (K) ke k (lCD)(C2H5)3NNONO8.6±4.03.21 + 0.166.3±4.24.5 ± 2.33.13 ± 0.163.7 + 2.64.1 + 2.10.084 + 0.0342.6 ± 1.9a temperature in kelvin; blanks indicate uncontrolled room temperature.b kexp from table 4.1, which equals the capture rate constant if capture is the rate limitingstep; ke and k determined from k and kjke from table 4.3. All rate constants inunits of 10_0 cm3molec’ s—i.average of a number of measurements, sometimes at different pressures.XeNON20NH3C2H4(CR3)4SiCH3NO2CH3HOCH3HOCF4CH3FCH3FCH3FC2H4FC2H4FC2H4FC2H4FHeHeHeHeHeHeHeHeHeHeHeHeHeHeHeHeHe1500228015002280d240022802280240095022801500240080017002400133083012.9 + 2.514.68 + 0.3620.0 + 2.234.7 ± 1.4398 25.0 ± 1.831.1 + 2.357.5 + 4.4406 31.5+2.5163 65.0 + 7.816.2 ± 1.433.0 ± 4.9398 26.5 ± 2.8128 47.7±3.414.0 + 4.9406 9.2±1.0208 18.7±1.6148 36.7+3.39.5 + 2.014.74 + 0.3710.3 + 1.230.3 ± 1.414.2 + 1.119.8 + 1.525.2 + 2.516.5 ± 1.331.8 ± 3.97.11 ± 0.7214.0 + 2.38.0 + 1.019.6 + 1.55.25 + 0.5810.43 + 0.9122.7 + 2.23.37 + 0.85—0.059 ± 0.0749.7± 1.14.37 ± 0.6110.70 + 0.8411.3 + 1.032.3 + 3.015.0 + 1.233.2 ± 4.19.09 ± 0.8718.9 ± 3.018.4 ± 2.028.1 +2.13.94 ± 0.448.27 + 0.7314.0 ± 1.5Ar 800Ar800dAr 400d selected from a number of measurements.85The differences between the kq values determined by the relaxations (table 4.1) andthe amplitude-based values (table 4.3) probably do not have a trivial explanation suchas impurities, but point to a more complex reaction mechanism involving capture, andstabilization of the excited intermediate complex. In other respects, the simple model(4.12) is sufficient for analyzing, interpreting, and understanding the data.4.5 A Mechanism with Capture and BreakupNot made clear in the reaction scheme (4.12) is that both charge transfer and muon transfer should proceed from a single reaction in which the molecule X is captured by the ion;i.e., what is missing from this simple model is any mention of ion—molecule capture. Forthe case where the capture (collision) rate is the limiting rate, the capture rate constantis just kexp from table 4.1. For such cases, capture is implicit in the simple model, andthese capture rates are listed in table 4.4, which also lists the rate constants ke and k,assuming kexp = = ke + k.To put this on a more rigorous basis, the capture can be shown explicitly in thereaction scheme:Mu+X+Mx+ )* XMu + M (4.19)MMu MMuXinvolving an excited ion (MMu+)*, which may be collisionally de-excited (with rate kq[M])or may capture a neutral reactant (k[Xj) to form an energetic intermediate complex(MM11Xj*. This is short-lived, and may undergo back-dissociation with or without energy loss (k, k), breakup into products (k, k), or collisional stabilization (k[M], k[Xj).86All of the final products except Mu in reaction scheme (4.19) are diamagnetic and areindistinguishable in the present experiments. Furthermore, many of these may dissociateinto smaller fragments which are themselves diamagnetic. Mu formation is the only causeof signal relaxation.It is clear from the outset that there are too many processes in this mechanism to useit directly in analyzing the data. Instead, various limiting cases of the full solution willbe examined, and these limits will aid in the interpretation of the fits already presentedin this chapter. Before presenting a complete solution to the capture mechanism, let usconsider the steady-state behaviour, when the complex is very short-lived and capture isthe limiting rate.The rate of depolarization due to Mu formation is given by the differential equations[Mu] = k[(MMuXj*] (4.20)0 = [(MMuXj*] = kc[X][(MMuj*] — (k + k + lc) [(MMuXj*] (4.21)[(MMuj*] k[(MMuxj*] (k[x] + kq[M]) [(MMuj*] (4.22)where= k + k[M] + k[X] + k (4.23)and the intermediate (MMuXj* ion is assigned a constant concentration by the steady-state approximation. Since X is very dilute, and the complex is short-lived, k can beignored. Solving for [Mu] gives the relaxation functionG ‘— [(MMuj*]o— [Mu]—[(MMuj*]o—1 kk[X](1—et) 424-- k[x](k + ) + kq[M] (k + k + k) (.where— k[X](k + k) k M 4 25-+ q[ ]. (.87The primed rate constants are undetermined and are for reactions of the complex;they all have higher order ‘overall’ counterparts given by k = kk’/ k’ which give theexpressionsG i — kD[X]+kq[M1 + ke[X]e’t 426)- (ke+kDl)[X1+kq[M1 ‘ (. )= (kD + ke)[X] + kq[M] (4.27)These are the same as the simpler model result, eqs. (4.16)&(4.13), except for kD replacing k,; therefore the k column in table 4.4 should rightly be interpreted as kD. Onemight hesitate to make a direct substitution because lCD = k + lCd + k[M] (+ kr[X1) isnot really a constant for varying [Xj or [M]. However, since kr[X] is undoubtedly muchlower than the other rates, it should be ignored, making kD constant with respect to [X]and so a viable substitute for k in the results presented thus far. The contribution ofstabilization can be (and was) determined separately by varying the moderator density,where kD/ke (‘kj/ke’) should increase with pressure. For most combinations at multiplepressures listed in table 4.3 the opposite trend is seen, indicating that k contributes verylittle. The only case with evidence of substantial stabilization of the complex is CH3F.Further results from varying [M] (pressure) at fixed [X] are presented in section 4.8.Another added reaction channel, dissociative de-excitation (kd), cannot be distinguished from muon transfer (kj, and since the ground-state MMu+ ion will subsequentlyreact by muon transfer anyway, the distinction between the two is almost meaningless.Finally, back-dissociation without de-excitation (kh) can reduce the observed totalrate constant kexp below the actual capture rate k, making it more difficult to differentiatebetween anomalously low collision cross sections and unstable complexes. Dissociationback to the original reactants, including the excited (MMu+)* ion, is somewhat hardto believe; production of ground-state MMu+, with rate constant kd, seems much morelikely. Since all of the neutral reactants studied should be much better quenchers thanHe or Ne [79,153—157], quenching of (MMuj* by the moderator cannot be important88whenever cyclic capture and breakup occurs: if k is significant, kq should be insignificant,and vice versa. For the neutral reactants that can only undergo charge exchange with anexcited ion, and which react below the theoretical capture rate (Xe, the fluoro-alkanes),an explanation with kb = 0 is to be preferred. For more easily ionizable neutrals, however,kb is expected to be more important than kd or kq.Since an excited state is not required for quite a few of the reactants studied, it isreasonable to consider reversible capture (kb), disregarding quenching of the initial ion inthose cases. If the MMu+ ion is presumed to react from the ground state just as well asfrom excited states, quenching is ineffective, and kq and kd (but not k) should be takenas zero. This presumption is not a good one, however. Instead, quenching should still beimportant, even when charge transfer is exothermic for ground-state reactants, since keis bound to be very sensitive to the degree of excitation above threshold.4.6 Complete Solution of the Capture MechanismThe exact solution to the complex’s concentration in the capture mechanism (4.19) is calculated by solving the coupled differential equations (4.21) and (4.22) (without the “0=”)to give[(MMuX+)*1= kc[X][(MMuj*]o (et — e_A+t) (4.28)where2 = k[X1 + kq[M] + k1 + k + k±/X1 + kq[Mj + k + k + k)2 — (4.29)V 4{k[X1(k + k’s) + kq[M](k + kb + k)}which leads to the relaxation envelopeG(t) =1- kkJX) + C[(et - e+t)(4.30)This shape is plotted as the solid line in figure 4.8, where the dashed line shows thenon-relaxing component and the dot-dashed line shows the simple exponential decay$9exp(—A_t). The deviation from the dot-dashed line is exp(—At). The interpretation ofthese components depends on the relative values of A2 kc[X1+kq[M] and A3= 0). This is easiest to see in the limit of k = 0 where A2 = A and A = A.A2 <<A3 : The case of the simple model (4.12) & (4.16) or the steady-state approximation to the capture mechanism where a very small constant concentration of complex israpidly reached, with ke = kk/(k + k3) and kD = kk/(k + kb), and the observedrelaxation (A2) is at k[X] + kq[M].A2 < A3 : This is the case where capture is the slower step, and the space between thesimple decay and the solid line is given by exp(—A3t)/A,corresponding to the build-upof the intermediate complex. No data was seen to exhibit this relaxation shape, although‘wall signals’ at slightly lower magnetic fields occasionally mimicked this dependence.A2 > A3 : This is the case where the complex break-up is the limiting rate. Even if thedeviation from exponential went unnoticed, the late tail does not depend on reactant concentration, contrary to the data. Furthermore, the intermediate complexes are expected0IIFigure 4.8 Relaxation shape for a capture mechanism with a long-lived complex( ). There are three components: a non-relaxing (A1 = 0) part ( ), an exponential decay (- . - -) corresponding to the rate in the simple model (A2 = k[X] + kq[M]),and subtracted from that, a faster decay at A3 = k + k + k. The actual relaxations donot appear to have this shape.Time90to be much too unstable for this situation to occur.This is the most uncertain case, with a relaxation shape going as (1 + )t) xexp(—)t) which may not be distinguishable from a pure exponential. However the rangeof relaxation rates usually measured should have been enough to reveal deviations froma simple relaxation, which were not seen.For the case of no equilibrium step (k = 0), the observed rate has no fall-off regimelike what is seen for a Lindemann mechanism; ) is given by sums of rates, not by a ratio. Nevertheless, as concentration increases, the observed (late-time) reaction rate doeschange from = k[Xj + kq[M] to the relatively constant )3 = k + k when =Although this is an abrupt transition, if the two exponentials of eq. (4.30) cannot beresolved experimentally, the results might resemble a slow transition from bimolecular tounimolecular kinetics as [X] increases. Such a transition cannot be considered a likelycircumstance though, because‘2 (capture) is expected to be the limiting rate at all Xconcentrations studied.Since no three-component relaxations were actually identified in the data, it is sensible to write a single overall relaxation (with a non-relaxing component) based on thismodel. Using the steady-state approximation has given equation (4.24) but a more general expression, reminiscent of the familiar Lindernann reaction rate, is found by takingthe low k[X] limit for ):k[X](Ic + k) + kq[Mj(k + k + k,) (4 31)— kc[X1+kq[M1+k+k:+kwith k = k + k[MJ + k{X] + k; but k = 0 and k = 0 must be considered likely, withthe complex mostly dissociating into products (k, k) or into de-excited reactants (k).The reaction rate (4.31) starts increasing with reagent concentration, but eventually levelsoff at high [X]. Some such curvature was observed for Xe + NeMu+, but not consistentlythrough the many repeated measurements. This special case is discussed in section 6.5.914.7 Other Possible MechanismsSome additional mechanisms deserve brief consideration, along with variations on theones that have already been presented.Multiple excited states: It seems quite unlikely that the ions NeMu and HeMu areformed in a single excited state, or that they are quenched to the ground state in onestep, although that is the approximation used in modeling the reaction. Given a varietyof excitation energies, the rate of (ground state) endothermic charge transfer is likely toincrease with the degree of excitation. For the case of two excited states contributing tothe reaction, and where charge transfer is faster for the higher excited state, there shouldbe a three-component relaxation: slow, fast (*) and very fast (**), as distinct from atwo-component relaxation. The states involved in this mechanism might be two differentvibrational levels, a vibrationally excited state and ground state (when charge transferis exothermic), or even an excited state of the molecular ion and a bare In contrastto the mechanisms featuring a buildup of an intermediate, the relaxation componentswould all be decays; i.e., the components are added, not subtracted. The extra component should be present even when capture has the same rate from both states, as longas ke/kD(*) < ke/kD(**). As noted already, the data do not generally exhibit this, orany other, three-component relaxation shape. This probably indicates that there reallyis only one ‘fast’ relaxation rate, or that the very fast component is too fast, in whichcase it can be completely ignored; but it might also mean that the two fast-relaxing components are similar and cannot be resolved, or that there are many components. Threeor more components could not be distinguished; instead, they would appear as some average relaxation rate. In the limit of a continuum of component rates, the result returnsto an exact exponential. Note, however, that there are far too few bound vibrationalstates of HeMu+ and NeMu+ (4 and 5 respectively) [75] to behave as a true continuumof excitation levels, although the rotational excitation could contribute as well. For, say,92two unresolvable relaxing components, the observed average rate would not vary linearlywith added neutral reactant. Such an effect was generally not seen.Note that the simple model (4.12) does not exclude multiple excited states, as longas capture is the limiting step for all states from which charge transfer can occur. Theremight be some deviation from that model’s prediction of A5/Af in the likely event thatke/k increases with increasing excitation, causing the amplitudes to vary more than thetotal rate constant with moderator pressure.Alternative reactions and fragmentation: Due to the nature of ILSR, the identification ofthe reactions (i.e., the reaction products) is not certain. This is especially true for the‘muon-transfer’ reactions which could have contributions from other reactions giving diamagnetic products. Most such reactions would actually involve muon transfer, but withsome degree of product fragmentation due to the great exothermicity of the muon-transferreaction and the resultant high product excitation. Table 4.5 shows some of the manypossibilities, with the reaction energetics calculated using the same vibrational zero-pointenergy corrections when substituting Mu for H in the reactants and the products. Sincethe rare gas ion reactants are less strongly bound than the products, this treatment isnot exact. Using harmonic zero-point corrections where the vibrational frequencies areknown (Cut, CHt, NH, and H3O [80]) raises the ZH of reaction by 0.1 eV.Since these reactions do not really affect the extraction of rate constants, and sincethe initial muon transfer is the same, such considerations will usually be ignored in theforthcoming discussion.In conclusion, despite the plethora of possible processes, the data are still bestdescribed by the simple mechanism (4.12) of a competition between charge and muontransfer reactions with X and quenching by M. The minor deviations from this do notaffect the fits to the data but can influence their interpretation. Capture is still implicitin this model, but the (unimolecular) rates of Product formation, k, k etc., cannot be93Table 4.5 Muon-Transfer and Fragmentation Reactions and Their EnergeticsReactiona /.H / eV for M = Ne HeMH + CH4 —* CH + M -3.6 —3.9—*CH+H2+M —1.7 —1.9+ C2H4 —* C2Ht —4.8 —5.1—* C2H + H2 —2.8 —3.0+ C2H6 —* C2H —4.1 —4.4—* C2H + H2 —3.4 —3.7—* C2H + 2H —1.4 —1.6+ NH3 —* NHt —6.8 —7.0—* NH + H2 —0.2 —0.4-I- H20 —* H3O —5.1 —5.4+OH+H2 2.1 1.9+ CF4 —* CF4H —3.4 —3.6—* CF + HF —2.8 —3.0H- CH3F —p CH4F —4.2 —4.4—f CH + HF —2.7 —2.9—* CH2F + H2 —2.6 —2.8+ CH3N —* CH3NH —6.1 —6.3+ CH4 + CN 3.3 3.1—> CH + HCN —1.8 —2.0+ CH3NO2—* CH3NO2H —5.7 —5.9—* CR4 + NOt —3.7 —3.9— CH + HNO2 —2.5 —2.7The reactions and reaction enthalpies are shown for NeH+ and HeH+ ions rather thanNeMu+ and HeMu+ on the assumption that the zero-point energy corrections are thesame for reactants and products. In fact, most of the products will have higher zero-point energies, raising /H by 0.1 eV, but most of the corrections are not accuratelyknown.94extracted from the data. Instead, the analysis, and the discussion, must be based on theapparent overall rate constants ke, k, etc. given by k = kk’/ k’. Cyclic capture andbreakup, when operative, invalidates the identity kexp = k, and provides one explanationfor the cases where kexp does not match the theoretical k. Dissociation with de-excitationis indistinguishable from muon transfer, and in fact will be followed by muon transfer, sokd will be subsumed in k, for the following discussion.Stabilization of the complex cannot be ignored because it has a moderator dependence (k[M}). This might cause some confusion because = k + k + k[M] is notconstant when [M} is varied, so ke and are not strictly independent of pressure if k ispressure independent. The variations are small, however, and can generally be ignored,except that kexp = ke + k + k[M] should actually be independent of total pressure. Thus,equations (4.13), (4.27), and (4.31) for the relaxation rate are best represented as= kexp[X1 + kq[M] (4.32)withkexp = ke + kD = ke + + k[M] (4.33)with the relative amplitudes— k k[M1+kq[M]4 34Af ke+ke ke[X1 (Values for ke and k in table 4.4 are best interpreted as ke and k + k[M}, respectively.Varying the moderator pressure can serve to elucidate the processes of stabilization andquenching.4.8 Pressure DependencesBesides varying the concentration of the dopant gas, studies were made varying the pressure (concentration) of the bath gas. Most of these were performed with neon because lowpressure helium offers too little stopping power tO the muons, limiting the experimentally95accessible pressure range. Table 4.1 shows a number of instances where the reaction rateconstant kexp was measured at two pressures, giving the same value in most cases, as isexpected from the simple bimolecular model (4.12). There are only two instances of apparent variations: The NH3+ HeMu+ rate constant appears to decrease with He pressure,but the 1500 torr measurement was performed long before the 2280 torr measurement,without cold-trapping the helium; the earlier (high, 1500 torr) result is not particularlytrustworthy. The other anomaly, CH3F in 800 and 1400 torr Ne, was questioned in section 4.2. According to the simple model, kexp = k should not vary with pressure, andthis is the observation in most cases, even for those, such as Xe in Ne, which gave resultswell below the capture (Langevin or AADO) predictions. It is possible that kexp woulddecrease due to quenching, but that is not easily accommodated by simple competitionkinetics. Results for xenon reported in this section an(l discussed further in chapter 6give weight to the CH3F and NH3 results.Other moderator dependences were measured by varying the moderator pressure fora single concentration of reactant. Since the observed relaxations do not have the extracomponents indicative of the more complex mechanisms, the following results were analyzed according to equations (4.32) and (4.33), where the (fast) relaxation rate, shouldincrease linearly with pressure (i.e., moderator concentration [M]) for a given concentration of dopant, with slope kq and intercept kexp[X] kjX]. Moreover, the relativeamplitudes AS/Af should increase linearly with [M], following eq. (4.34). Table 4.6 liststhe parameters determined by linear fits to the relaxation rates and amplitudes for anumber of runs varying the moderator pressure with a constant concentration of neutralreactant. Although these values are not as extensive as those determined by varyingconcentrations of X (table 4.1), they do provide additional insight to the details of thereactions.As predicted, the relaxation rates generally increase with added moderator, althoughthe variation is small. But there is one obvious disagreement with the mechanism: for96Table 4.6 Results from Varying the Pressure at Fixed [X]relaxations amplitudesW X [X]b kexpC kqd kjjkee ks[X1+Icq k9Ne NH3 various’ 20.7±2.2 14.0±4.3 0.030+0.030 10.0±1.1Ne Xe 44.5 5.91+0.49 —12.3+4.0 —0.482±0.051 65.0+4.6O 8.16±0.65Ne Xe 14.4 9.10+0.28 —6.66+0.82 —0.002±0.016 2.68+0.48 6.32±0.65Ne Xe 50.5 6.26+0.38 —20.3+2.9 0.066±0.024 6.2+2.3 4.74±0.64Ne CH3F 12.8 18.4+1.8 5.5+4.3 0.143±0.054 40.9+2.0 47.1±6.8He CH3F 6.06 28.7+10.1 28+13 0.78±0.28 190+40 460±220Ar NO 32.5 2.8+2.6 58+34 0.34+0.23 45+29 —15±11Ar NO 16.3 2.6+3.0 34+21 0.13+0.38 46±25 —14±15a The moderator gas whose pressure was varied; also a component in the molecular ionMMu+. All these results were measured at room temperature and fitted using equations(4.32), (4.33), and (4.34).b Concentration of the neutral reactant, X, in 1014 molec cm3.The total rate constant, kexp k in units of 10_b cm3mo1ec s, determined fromthe intercept of A vs. moderator pressure p. Compare with values in table 4.1.d Given by the slope of A vs. p; in units of 10_15 cm3 ino1ecs1.The (dimensionless) p = 0 intercept of AS/Af vs. p.f 106 times (k[Xj + kq)/ke determined by the slope of A/Af vs. p.Ic5 in units of 1 0° cm6molec2s’, calculated from other values in this table. Usingthe values of ke from table 4.4 gives similar results. k5 = 0 is expected for NO in Arbecause stabilization of ArMuNO still leads to depolarization.h The three NH3 concentrations gave scattered results; reported here is a simultaneousfit to all points.Values from fits with the intercept constrained > 0.97Xe in Ne there is a consistently negative pressure dependence of the relaxation rate, asshown in figure 4.9. It makes intuitive sense that increased quenching at higher pressureswould reduce the rate of an endothermic reaction, but such behavior is hard to reproducewith a simple kinetic model. The first measurement ([Xe] 44.5) deviates from the trendset by the latter two mainly in being shifted up, closer to the 50.5 values; if the trend inthe slopes of the three lines can be believed, kq becomes more negative with increasing Xeconcentration. This particular result will be analyzed further in section 6.4. The inversepressure dependence does agree with the variation in kexp seen for CH3F, but not withthe constant value measured for Xe.The value of kexp = 20.7 x 10_b cm3molec’ s1 for NH3 (from the intercept of thesimultaneous fit of ) vs. p) agrees moderately well with the value of 26.4 in table 4.1,but fitting ) vs. [NH3] for each of the four pressures independently and averaging theresults gives the value of 26.6 reported for “various” pressures in table 4.1, in remarkableagreement with 26.4. The kq for NH3 in table 4.6 agrees well with the values in table 4.1,3.53.02.5r2.0U,1.51.00.50.00 500 1000 1500 2000 2500Ne Pressure (torr)Figure 4.9 Neon pressure dependence of the fast relaxation rate for three concentrations of xenon: 50.5 (.), 14.4 (.), and 44.5 () x iO’4 moleccrn3. The 44.5 line wasmeasured in an earlier run period than the other two.98from the intercepts of ) vs. concentration, but are much higher than those in table 4.3,derived from the amplitudes vs. [NH3].The relative amplitudes A/A vary strongly with pressure more strongly thanwould be expected from kq alone. An example is shown in figure 4.7(c, d) for CH3F +NeMu. This difference is attributed to stabilization of the complex, which affects therelative amplitudes, but not the overall relaxation rates. Values for k were calculatedthis way and are shown in table 4.6. (Note that these are the overall termolecular k, notthe bimolecular k.) All the values seem reasonable, although the ones for Xe are probably inflated due to the anomalously negative values for kq. Even the slightly negativek values for NO in Ar are acceptable because stabilized ArMuNO+ is paramagnetic andshould still give depolarization; thus, a measured k5 = 0 is expected.The first series of runs for Xe gave a significantly negative value for k,/k6 as azero-pressure intercept of AS/Af, but the points are badly scattered; the other Xe measurements had intercepts consistent with zero, while the NH3 results, measured at thesame time as the anomalous Xe results, were extremely scattered. The Xe amplitudesgave reasonable results with the intercept (k.u/ke) fixed = 0, and the NH3 results were allfitted simultaneously to give the quite acceptable results in table 4.6. The values of kii/kefor Xe and NH3 agree well with the low k0/ke = (k + ks[M1)/ke values listed in table 4.3determined by the variation of amplitude with [Xe] and [NH3].The [M] = 0 intercepts of the amplitude for CH3F give notably smaller values ofk,jke in table 4.6 than the corresponding kD/ke values determined by varying the CH3Fconcentration (listed in table 4.3 and visible in figure 4.7), indicative of a substantial k:k= ( — ) Le = 12.6 ± 5.3 x i0° cm6molec2s’ . (4.35)This result is in disagreement with the value (47±7) in table 4.6, but the difference maynot be significant given the uncertainties and the general level of variation. It is againnoteworthy as well that kexp for CH3F appeared to vary with Ne pressure.99Both the relaxations and amplitudes of the NO/Ar data are too uncertain to saymuch about. This uncertainty is mainly due to the lower diamagnetic signal amplitudein Ar, resulting from epithermal Mu formation. Nevertheless, the values for k were neartheir expected values of zero.These results are important in assessing the mechanisms and extents of excitationand quenching in these reaction systems. Most importantly, it was found that stabilizationof the capture complex (ks) could be important (for CH3F and Xe) but not universally so.Additional measurements of quenching were performed with ternary mixtures of argonplus neon plus ‘X’ but these will be presented as part of the discussion of quenching inchapter 6. Presentation of other ternary mixture measurements is also deferred until theycome up in discussion. The results of pressure dependence measurements have generallyagreed with the results presented earlier, but have served to illuminate the importanceof quenching the intermediate complex, as distinct from quenching of the initially excited ion.4.9 Slow Relaxation RatesAlthough the kinetics of the slow relaxation rates are unrelated to the mechanisms invoked to interpret the fast relaxations, it seems worthwhile at least to tabulate the slowrelaxation results. Table 4.7 lists the slopes (k10) and intercepts )) for linear fits ofthe slow relaxation vs. reactant concentration in helium and neon at room temperature.A number of reactants are listed for which there was no ‘fast’ relaxation, so their overallrelaxation rates were taken as ; and there are some reactants missing from the tablebecause they had slow components of very small amplitude. In about half the systems,the added reactant had a significant effect on the slow relaxation; these are marked bydaggers and asterisks in table 4.7. The daggers signify that was similar to the relaxation seen in pure moderator, while asterisks indicate that shifted to a higher value(with or without a significant k10).100Table 4.7 Rate Constants for the Slow Relaxation in He and Ne ModeratorsReactant Moderator pa ki0b A00.01801 + 0.000870.0151 + 0.00240.0135 ± 0.00110.0301 + 0.00100.0330 ± 0.00150.033 ± 0.0150.0139 ± 0.00110.0731 ± 0.00200.0195 + 0.00720.01530 ± 0.000800.0139 ± 0.00110.0340 ± 0.00250.0316 ± 0.00140.095 + 0.0160.0323 ± 0.00360.0271 ± 0.00690.01950 + 0.000700.0674 + 0.00150.0321 + 0.00340.0171 ± 0.00150.080 ± 0.021 *0.0541 ± 0.0051 f0.0267 ± 0.0029 f0.047±0.017 *0.0488 ± 0.0068 *0.02050+0.00080 t0.1145±0.0069 *0.0743 ± 0.0025 fa The moderator pressure in torr, at room temperature.bThe slope of ) vs. reactant concentration, in 100 cm3molec’ s1.The zero-concentration intercept of the line, in s1. When this differs substantiallyfrom the relaxation rate in pure moderator the number is followed by an asterisk (*);when the intercept is the same, hut there is a substantial slope, a dagger (t) is shown.•1•1tt*Kr Ne 1000 0.0010±0.0027Xe Ne 1300 0.002 + 0.022Xe Ne 1000 0.166+0.092CO Ne 800 —0.0047 + 0.001502 Ne 800 0.038 + 0.049NO Ne 800 0.72 + 0.25N20 Ne 1000 0.012 ± 0.022NH3 Ne 800 —0.052 + 0.038NH3 Ne 1300 —0.059 + 0.054CR4 Ne 1000 0.0137 + 0.0061C2H4 Ne 1000 0.056 + 0.019(CH3)4Si Ne 800 0.0005 + 0.036CH3NO2 Ne 800 —0.102 + 0.029CF4 Ne 800 0.082 ± 0.046CH3F Ne 1400 0.000 + 0.017CH3F Ne 800 0.047 + 0.057Kr He 2280 0.00095 + 0.00036Kr He 1500 0.00024 + 0.00084Xe He 1500 0.032 + 0.031CO He 2280 0.00006 + 0.00058NO He 2280 0.053 + 0.014N20 He 1500 0.069 + 0.023NH3 He 1500 0.154+0.052NH3 He 2280 —0.23 + 0.18(CH3)4Si He 2280 —0.269 + 0.074CH3NO2 He 2280 —0.189 + 0.028CF4 He 2280 0.111 + 0.042CH3F He 1500 0.103+0.017101Most of the rate constants are consistent with zero, but a few are significantly different, both positive and negative. (The negative values indicate k510 is not really arate constant.) The reproducibility is generally good for repeated pairs of reactant andmoderator, with the possible exception of NH3 in He. Nitromethane is the only reactantthat gave a negative dependence in both He and Ne; CO and (CH3)4Sieach had a negativeslope in Ne and He respectively. Although there are three negative values of k10 listedfor NH3, all are consistent with zero. The “significant” slopes, both positive and negative,could be ascribed to the random distribution of values near zero, but there does seem tobe a real effect on in some cases. Strangely, this effect seems to be much stronger inhelium bath gas than in neon; four of the reactants give increased in He, with CF4’sbeing the highest, but only CF4 has any visible effect in neon. This hints that the processresponsible involves collisions with the moderator, e.g., XMu+ + He collisions.Given the distributions of both positive and negative values for k10, and the lackof any real trend in ‘significant’ values, there is no chance of elucidating the slowrelaxation mechanism from the present results. If there is any contribution from collisional relaxation mechanisms, it is probably well masked by the inevitable relaxationdue to magnetic field inhomogeneity. The apparent offsets () can easily be attributedto parameter correlations when fitting two-component relaxations as opposed to single-component fits for the pure moderator runs.4.10 Total Diamagnetic AmplitudesAnalysis of the total diamagnetic amplitudes, Af + A, relates to processes occurring during thermalization rather than to thermal kinetics, but the results prove interestingin themselves, and can even shed some light on thermal charge transfer forming Mu.Since, as discussed in chapter 1, He and Ne have ionization potentials (IP) muchhigher than Mu (24.587 and 21.564 eV vs. 13.5 eV [81]), and subsequently have very lowcross sections for epithermal Mu formation and high cross sections for Mu loss, all the102+ polarization observed in these inert gases is in a diamagnetic environment [44, andthis thesis]. As small quantities of more easily ionizable gas are mixed with the noblegas, some Mu is observed; and eventually, only Mu is observed. Figure 4.10 shows thiseffect for a number of gases used in this thesis, and demonstrates the different effect ofeach gas.The thermalization of Mu and in a mixture of X and M can be loosely represented by1[M} DM o[M] MuP + (4.36)3Ixl4[X] Dwhere the muon-bearing precursor P, at some arbitrary initial energy, can eventuallyI I I1.0-CF4+ 0.8-Kr0.6--CH3NO2 N20-0.2- (CH3)4SiXe -0.0 I I I I0 20 40 60 80 10014 —3[X] (10 molec cm )Figure 4.10 The variation of diamagnetic amplitude AD = Af + A with reactant gasconcentration [X] in neon moderator, due to Mu formation by the various reactants. Thewide variety of Mu-formation effectiveness is reflected in the values of 3 varying from 0.35for (CH3)4Si (IP = 9.8 eV) to 5.5 for Kr (iP = 14.0 eV). Most 0 but for CF4, ,6 = 3.103thermalize as Mu or in a diamagnetic species D after collisions with the reactant gas Xand the moderator gas M (M = He, Ne). For a diamagnetic P, particularly the fourcollisional processes are: thermalization by moderator collisions (o), muonium formationby charge exchange with M (2), muonium formation by charge exchange with X (o),and thermalization or production of other diamagnetic species by collisions with X.Actually, o- and o4 are cross sections only in the vague sense that o, for example, isa velocity-independent rate constant for the kinetic thermalization ‘reaction.’ There arethree possible processes that contribute to a: for P = p4 there are MMu+ formation andsimple thermalization, and for P = MMu+ there is MMu+ thermalization.In order to do calculations based on this model of thermalization, the ratios of therates or cross sections will be assumed constant over the energy range of interest. Withthis condition, the concentration of diamagnetic species after full thermalization is[D] — [P]0 (o1[M] +u4[X])— 1[M] + 2[M] + u3[Xj + 4[X]Since this equation is over-determined, and only the ratios of rates matter, one shoulddefineAD=Ao[D]0j[P]o, /3_u1a, !3X°4/3, IM=a2/ol (4.38)to giveA —A ,3[M]+/3x[X] 4D— °[M] + M[M] + [X] + x[X]where AD is the experimental total diamagnetic amplitude, and A0 is the total of allamplitudes: A0 = AD +2AM.Equation (4.39) is still over-determined, however, and it can only be used to fitthe experimental amplitudes if one or more parameters are known a priori. For purehelium and neon moderators, all the signal is diamagnetic, so 13M = 0 and A0 = ADwhen [X] = 0. A similar assessment can often be made for /9x which should be given104Table 4.8 Fits of Total Diamagnetic Amplitudes at Variable Reactant ConcentrationsReactant IP (eV) M p(torr) T(K) A0 ,3bKr 14.00 Ne 1000 0.2705 ± 0.0018 3.88 ± 0.55 0.165 ± 0.093Kr Ne 800 0.2826 + 0.0010 5.54 ± 0.61Xe 12.13 Ne 1300 0.2537 ± 0.0038 1.85 ± 0.17Xe Ne 1000 0.2664 + 0.0021 2.7 + 1.5Xe Ne 800 0.2902±0.0083 1.23 ±0.10Xe Ne 1400 445 0.3465±0.0021 1.413±0.036Xe Ne 565 179 0.3563 + 0.0027 2.085 + 0.066 cXe Ne 370 117 0.3252 + 0.0032 1.131 ± 0.072Xe Ne 1000 117 0.3353+0.0022 1.07±0.11CO 14.01 Ne 800 0.2850 + 0.0020 6.42 + 0.3102 12.06 Ne 800 0.284 ± 0.011 2.14 ± 0.76 dNO 9.26 Ne 800 0.2844 + 0.0022 2.90 ± 0.18 cNO Ne 800 0.2684 ± 0.0010 2.94 ± 0.26N20 12.89 Ne 800 0.2684 + 0.0010 1.69 ± 0.11N20 Ne 1400 445 0.3460 ± 0.0021 1.854 + 0.089N20 Ne 567 177 0.3539 + 0.0030 1.81 + 0.34 0.79 + 0.40NH3 10.16 Ne 800 0.2535 + 0.0029 1.60 + 0.19NH3 Ne 1300 0.3015 ± 0.0070 2.56 + 0.71NH3 Ne 1400 445 0.3454 + 0.0019 1.713 ± 0.089NH3 Ne 567 179 0.3534 + 0.0028 2.91 ± 0.46CH4 12.51 Ne 1000 0.2716 + 0.0017 1.134 ± 0.055 cC2H4 10.51 Ne 1000 0.2673 + 0.0021 1.391 + 0.092 c(CH3)4Si 9.80 Ne 800 0.2853 ± 0.0025 0.353 ± 0.014 cCH3NO2 11.02 Ne 800 0.2865 + 0.0022 0.772 + 0.042 cCH3NO2 Ne 1300 406 0.2553 + 0.0010 0.770 + 0.042CH3NO2 Ne 740 223 0.2509 ± 0.0012 1.134 + 0.081CH3N 12.19 Ne 1300 406 0.2552 ± 0.0010 0.419 + 0.018CF4 13. Ne 800 0.2847 ± 0.0023 2.7 ± 1.4 3.0 + 1.1Continued...105Table 4.8 (continued)Fits of Total Diamagnetic Amplitudes at Variable Reactant ConcentrationsReactant IP (eV) M p(torr) T(K) A0 /3CH3F 12.47 Ne 1400 0.2823 + 0.0053 1.64 ± 0.16 cCH3F Ne 800 0.2575 + 0.0360 0.50 + 0.76 0.51 ± 0.17CII3F Ne 1400 445 0.3469 ± 0.0020 0.959 ± 0.089 0.42 + 0.11CH3F Ne 700 179 0.3557 + 0.0028 1.359 + 0.056Kr 14.00 He 1500 0.2838 + 0.0049 8.6 + 2.6 0.47 ± 0.24Kr He 2280 0.3241 ± 0.0018 11.4 ± 1.6 0.37 + 0.23Xe 12.13 He 1500 0.2658 + 0.0057 4.9 ± 2.9 cCO 14.01 He 2280 0.3249 ± 0.0021 10.2 ± 4.7 2.9 ± 1.3N20 12.89 He 1500 0.2762 ± 0.0066 7.4 ± 3.9 dH2O 12.61 He 2280 0.3256 + 0.0016 3.02 + 0.15 eC2H6 11.52 He 2280 0.3246 + 0.0019 2.63 + 0.19C2H4 10.51 He 2400 398 0.2545 + 0.0067 7.4 + 7.4 e(CH3)4Si 9.80 He 2280 0.3248 + 0.0020 1.85 + 0.54CH3HO 10.23 He 2400 406 0.2657 + 0.028 0.88 + 0.26CH3HO He 950 163 0.2594 + 0.0013 3.1 ± 1.1 dCH3F 12.47 He 1500 0.2778 + 0.0038 16. + 17. dCH3F He 2400 398 0.2608 + 0.0060 3.8 + 1.5 eCI-13F He 800 128 0.2672 + 0.0054 9. + 15. eC2H4F 11.87 He 2400 406 0.2753 + 0.010 1.67 + 0.53C2H4F He 1330 208 0.2686 + 0.0012 4.9 ± 1.3 dC2H4F He 830 148 0.2639 ± 0.0071 —2.6 ± 2.0 ea The relative efficiencies of muon thermnalization and molecular ion formation by themoderator versus muonium formation by the reactant X; 3 =b The rate of formation of diamagnetic products by X relative to the rate of Mu formation; /9x = u4/u3. Blank entries are zero; either because the fit gave that result, or forthe reason noted.The fit gave a negative 13x, so it was constrained to be zero.d Poor results could not reasonably determine three parameters; /3 was fixed at itsexpected value of zero.Results were nearly constant and were fitted by a linear regression, taking 3[M] =—intercept/slope.106by the ratio of diamagnetic to muonium fractions in pure X. However, although Mu hotatom reactions generally give rise to --‘20% diamagnetic tSR signal in pure moleculargases [38,89,90], such reactions should be greatly suppressed in the present experimentsby the vast excess of inert moderator. Thus, the muon fractions observed in pure X areprobably not a good indication of /3x; instead, for molecules whose IP is below 13.533 eV,100% Mu formation is expected at sufficiently high concentrations, so /3x can be set tozero when necessary. Table 4.8 lists the results of fits to equation (4.39), all of which had/3M set to zero, and some also had /3 = 0 assigned. The reproducibility and precisionof the parameters are quite good for Ne moderator, but somewhat worse for He; thereproducibility of 3 is poor for CH3F (in He and Ne) and for C2H4F.The interesting parameter is 3, which measures the efficiency of muon thermalization and/or molecular ion formation by M relative to muonium formation by X. Forboth Ne and He moderators, the values of /3 for CO and Kr stand out as the highest. This is is the expected result based on those molecules’ high ionization potentials,which make Mu formation unfavorable. Is the converse also true? Although there aresome low values of /3, for (CH3)4Si, CH3NO2,and CH3N, there seems to be no correlation with IP. Why should CH3N (iP = 12.2 eV) have a low /3 while NO and C2H4(iP = 9.3, 10.5 eV) do not? An answer may be that all these molecules can form Mu rightdown to thermal energies, so their 1P’s are not an issue. Instead, the low-,3 molecules arethose with the highest polarizabilities and dipole moments, indicating that their capture(collision) cross sections for determine their epithermal Mu-formation cross sections.This is what one would expect if the final Mu formation occurs at quite low energy, saybelow 1 eV.An interesting exercise is to compare 3 in He and Ne for a given X. The averagevalues of /3 were taken for each X & M pair, the ratio /3(He)//3(Ne) was taken for every Xthat had /3 determined in both He and Ne, and all those ratios were averaged to give(/3(He)/,6(Ne)) = 2.40 +0.35. So what is the meaning of this number? Recall /3 =107where €73 is independent of M, so/3(He) u1(He)u3(Ne) = o-1(He) (4 40)3(Ne) a1(Ne)u3(He) o(Ne)Now it is time to define the ‘thermalization reaction’ and cr better. The pseudo-cross section is best represented as a collision cross section o multiplied by an energyloss factor e, the average energy loss per collision, so = ue. This is related to thestopping power of the moderator, dE/dx = o n v, (the number density n is generallyreferred to as concentration [M] in this thesis). The energy range of importance is set bythe energy of final Mu formation by X (the competing process), which for the mixturesin question probably extends from thermal up to a few eV kinetic energy [44,85,91, andmentioned above], but well below the energy for Mu formation in pure He ( 100 eV)and Ne ( 60 eV) [85], where no Mu reaches thermal energies. The characteristic energyis thus independent of whether the moderator is He or Ne, depending only on X. Sincecollisions with Ne and He should be elastic in the thermal-to-few-eV range, and assumingisotropic scattering, the energy loss is a purely kinematic factor,= E (i — M2 + m2 (4.41)(M+m)1where M and m are the masses of the colliding species. For the case of molecular ionthermalization, M m, and = E/2. This is much too high to have a viable competition between Mu formation by X and thermalization by M— once the molecular ion isformed, it is thermalized in just a few collisions. For the case of thermalization inneon, = 0.011 F, and in helium, = 0.052 F, so,8(He) u1(He)— (He) E(He)— 4 8(He)4 42/3(Ne) — a1(Ne)— u(Ne) E(Ne) — a(Ne).The elastic cross sections a for protons in He and Ne have been measured [94] at low energies, and their ratio is likely indicative of the ratio for muons [85,86]. The cross sectionslevel off and converge somewhat below 10 eV, and their ratios are a(Ne)/a(He) = 1.9 at1081 eV and 2.8 at 10 eV, giving values for /(He)//3(Ne) = 2.4 and 1.7 respectively. Theseare both in excellent agreement with the average value of 2.4 arrived at above, with the1 eV value agreeing exactly! Given the approximations involved, though, it is not reallypossible to pin down the exact energy range, but it does indicate that the thermalizingspecies is a bare reinforcing the picture of some Mu formation during thermalization, followed at low kinetic energy by the remaining attaching to a moderatorgas atom to form a muonated molecular ion. The muon kinetic energy at the point ofmolecular ion formation is probably less than 0.5 eV, based on the discussion above andon studies of Hf—He scattering [158].As an alternative to thermalization in this scheme, there is the process of epithermal molecular ion formation, which might compete with Mu formation in a similarway. The cross sections for this association are not known, but the Langevin value is= irq-/7E which would give 3(He)/3(Ne) = 0.72 — somewhat lower than measured. As just mentioned, the association reaction would not happen above 0.5 eV [158],whereas most Mu formation is already finished at this energy—the Mu that forms does soat higher energies than molecular ion formation. Although ion formation does not directlycompete with the bulk of Mu formation, the Mu-formation regime will be terminated bycreation of a molecular ion which is then thermalized very rapidly.In an earlier paper [27], two ways of forming NeMu+ were suggested:+ Ne +u + Ne —* NeMu (4.43)Mu* + Ne —f NeMu + e. (4.44)The latter process need not have a third-body collision because two separate productsare formed, while the former requires collisions by the moderator to stabilize the NeMu+ion. However, since the Mu must be ionized in the second reaction, it must involve quitea high (kinetic) energy Mu, ‘s.’ 10 eV. The measurements presented in this section haveshown that the first process, eq. (4.43), is clearly the correct one.Chapter 5KINETICS DISCUSSIONIn the previous chapter, kinetics results for the reaction of HeMu+, NeMu+, ArMu+, andN2Mu+ with a wide range of neutral species were presented. Various reaction models weresuggested to interpret the results, with the simplest viable model being the mechanism(4.12) of competing collisional de-excitation, Mu formation, and transfer from avibrationally excited MMu+. More detailed models were considered, but they could notbe used for data analysis without simplification. One supplement to the simple modelwas found necessary: stabilization of the capture complex, with the overall rate k[X][M].With this addition, the mechanism agreed very well with the data, and this situationwill be reaffirmed in the following discussion. Nevertheless there are some features of themeasured data that require consideration of modified mechanisms, although the rates willstill be parameterized in terms of the simplified model, equations (4.32)—(4.34).Another topic to be covered is the role played by the initial excitation and subsequent quenching — processes which must be present but are not clearly defined by thedata. Before dealing with the excitation of the reacting ions, though, it is necessary toshow that the ions are indeed the muonated rare gases HeMu+, NeMu+, and ArMu+.1091105.1 Identification of the Reacting IonsA restriction of the basic iSR method employed for this research is its inability to identify different closed-shell or diamagnetic species. In the more common study of Mukinetics, the reacting species is definitely known to be the Mu atom based on its distinct spin precession frequency [97,99,103], although the reaction products must oftenbe identified with reference to theory or the analogous H-atom experiments [30,82,102].Identification of paramagnetic products has been achieved by observing level-crossing resonances [159—161], or by the characteristic precession frequencies if the reaction is fasterthan the precession period [159,162]. Diamagnetic products can be identified as suchby RF resonance techniques [163], although this does not distinguish between differentdiamagnetic species since chemical shifts are usually far too small. None of these specialized techniques is amenable to the experiments at hand, and no product analysis wasperformed.In the present measurements, the experimental signal is at a diamagnetic frequencyso the initial species is not strictly determined. As described in chapter 1, there arefour situations that give rise to such a precession signal: a bare a (diamagnetic) +molecular ion, a muonium-substituted (diamagnetic) molecule, or a paramagnetic speciessuch as Mu or a Mu-substituted radical undergoing very rapid spin exchange [164]. Theresults presented were already attributed to molecular ions, but the other possibilitiescan be considered now, and eliminated.The case of fast spin exchange can be rejected immediately because there is no highconcentration of paramagnetic molecules to exchange spin with. This is true even in thecase of 02 and NO dopants, which were always used in low concentration.Muonium-substituted molecules, such as C2H5Mu, are commonly formed by reactions of molecular gases with Mu in the few-eV range, but while molecular species mightaccount for the lack of relaxation in H2 and C2H6 moderators, there are no such closed-111shell neutral molecules that could be formed in He, Ne, Ar, or even N2. Even with theaddition of reactive dopants to the inert gases, the preponderance of inert gas moderatorwould serve to minimize hot atom reactions with ‘X’ by thermalizing Mu through theenergy range where those reactions occur. Furthermore, whatever effect the added reactants have, they could not contribute to the 100% diamagnetic signal in pure He and Nemoderators.The case of a bare could not be dismissed a priori, although it was deemed veryunlikely [1.3, and ref. 44] given muon affinities of 1.5eV (for helium) and higher [22,144].The general lack of reaction in Ar, N2, H2, and C2H6 indicates that, at least for thesegases, the muon is not free; rather, it is bound in a molecular ion. This still leaves thepossibility of a bare in He and Ne, where the low polarizabilities and lower muonaffinities might make capture inefficient. The measured reaction rates, however, ruleagainst this possibility. As seen in table 4.1, the reactions are consistently faster in Hethan in Ne, consistent with the higher collision frequency of lighter (and faster) HeMu.The expected ratio is given by the square roots of the reduced masses of each X + MMu+system; for a heavy neutral, the ratio is kHeMU+/kNeMu+ = \/20.1/4.1 = 2.2 [see equations (3.7) and (3.13)], which agrees well with the values measured. A bare wouldreact at the same rate in both moderators, but much faster than actually seen: 6 timesfaster than HeMu+ and a stupendous 13 times faster than NeMu+. Since (as described insection 5.2) the present results agree with established capture theories, the reactive diamagnetic species in the rare gases and N2 is clearly the muonated rare gas molecular ion,rather than a neutral molecule or bare muon.5.2 Comparison With TheoryA comparison of the experimental (room temperature) rate constants is presented in tables 5.1 through 5.3. Table 5.1 compares the rates for non-polar neutral reactants withthe Langevin predictions for both HeMu+ and NeMu+ ions. Cases where no reaction112was evident are noted. ArMu+ showed no relaxation with Xe, H2, 02, or (CH3)4Si, andN2Mu+ showed none with C2H4 or 02. Experimental results for dipolar molecules arecompared with theoretical dipole capture rate constants, as calculated by various methods, in table 5.3. Table 5.2 lists the parameters used for calculating the theoretical rates;some of the parameters chosen should be commented on.The polarizabilities are average-orientation (isotropic) values taken mostly from general references [150,165], which were determined by index of refraction and dielectric constant measurements. Judging by the disagreements among sources, there is substantialuncertainty in these values. The polarizability of (CH3)4Si was not listed and so wascalculated from the index of refraction [166] using the Lorentz and Lorenz (Clausius—Mosotti) equation [166]. A value of 7.37 A3 reported [150,165] for nitromethane is fromthe dielectric constant measured at too low a frequency [165], so a value of 4.94 was calculated from the index of refraction. Neither the polarizability nor the index of refractionwere available for difluoroethane, so was estimated from the trends in similar molecules.Note that the high-frequency polarizability calculated from the index of refraction is themore appropriate measure for ion—molecule capture because low-frequency measurementshave a contribution from the dipole, which is treated separately in the capture theories.The moments of inertia (I) were mostly derived from rotational spacings of spectra [167], but I for CH3F, C2H4F,CH3NO2 and (C2H5)3N were calculated from bondlengths and angles [168,169]. For (C2H5)3N, NH3, and C2H4Fthe axis of rotation chosenfor calculating I was not the principal rotation axis, but one perpendicular to the dipole.This is a matter not dealt with in the literature, where a linear molecule is usually assumed, but it seems reasonable, except perhaps for the quantum treatments. In any case,the moment of inertia has only a small effect on the calculated rate constant so it is notcritical that it be precisely known.The comparison between theory and experiment in tables 5.1 and 5.3 reveals agreement over a wide range of l)OlariZability, (lipole moment, and exothermicity, with experi113Table 5.1 Experimental Rate Constantsa for Non-Polar Neutrals Reacting with HeMuand NeMu+ Compared with Langevin Capture RatesHeMu+ NeMu+Reactant (A M (amu) kexp kL kexp kLaKr 2.484 83.80 c 18.65 0.56 + 0.11 9.13Xe 4.044 131.3 12.9 + 2.5 23.59 5.35 ± 0.28 11.23H2 0.805 2.016 c 18.06 c 15.5102 1.581 32.00 — 15.43 6.43 + 0.37 8.36C114 2.593 16.04 c 20.85 c 12.60C2H6 4.47 30.07 c 26.04 c 14.23C2H4 4.252 28.05 25.0 + 18d 25.51 18.6 + 3.5 14.07(CH3)4Si 12.0 88.23 31.1 + 2.:3 40.92 16.2 ± 2.4 19.97CF4 3.838 88.00 16.2 ± 1.4 23.15 6.59 ± 0.47 11.30a All rate constants in 10_b cm3molec1s1.bIsotropic polarizability in A3, from [150,165], except for (CH3)4Si where the value of12.0 was calculated from the index of refraction and density of the liquid [166].No relaxation observed. Other non-polar combinations that showed no relaxation areArMu plus Xe, H2, 02, and (CH3)4Si; and N2Mu plus C2H4 and 02.d Measured at a temperature of 398 K; all others were measured at room temperature,295K.114Table 5.2Parameters for Dipole Capture CalculationsNeutral a a ltD M C J C TR(300)dNO 1.70 0.153 30.01 0.01641 6.025N20 3.03 0.167 44.01 0.06675 9.002NH3 2.26 1.47 17.03 0.00282 0.08666H20 1.45 1.85 18.02 0.00301 0.03511CH3F 2.97 1.85 34.03 0.03274 0.07190C2H4F 4.5 2.27 66.05 0.15930 0.07236(C2H5)3N 13.1 0.66 101.19 0.48600 2.492CH3N 4.48 :3.92 41.05 0.09115 0.02416CH3HO 4.49 2.69 44.05 0.08250 0.05141CH3NO2 4.94 :3.46 61.04 0.13840 0.03419a The isotropic polarizability of the molecule in A3, from [150,165], except for C2H4Fwhose value was estimated from similar molecules, and CH3NO2for which the value of7.37 was rejected as too high (see text) and the value of 4.94 was calculated from theindex of refraction and density of the liquid [166].bThe electric dipole moments [150,166], in Debye (lO18esucm).C The masses (in amu) and moments of inertia (10 g cm2). Values for I were takenfrom tabulated spectroscopic parameters [167] or calculated from molecular geometries [168,169]. In calculating I, an axis perpendicular the dipole was chosen ratherthan the axis of greatest I.d The reduced temperature, TR = 2akT/1t, for T = 300 K.115Table 5.3Comparison of Experimental Rate Constants with Various Capture Theory PredictionsReactants kexp ktiieoryaLOS LD ADO AADO CT VTST SACMHeMu + NO 14.68 + 0.36 16.07 23.46 16.75 17.30 16.95 19.06 10.93N20 20.0 ± 2.2 21.02 28.93 21.65 22.62 21.92 24.72 14.01NH3 34.7 ± 1.4 19.34 93.52 37.37 39.60 43.32 47.89 39.88CH3NO2 57.5 ± 4.4 26.52 188.40 68.65 92.54 84.83 96.81 82.96CH3F 33.0 + 4.9 21.07 109.77 43.02 51.04 50.53 56.13 47.16C2H4F 14.0 ± 4.9 25.25 131.20 51.45 68.28 60.41 67.10 56.75H20 b 15.41 108.26 39.53 42.74 48.78 55.61 47.89CH3HO c 25.60 152.97 57.97 73.58 69.68 78.24 66.16NeMu + NO 8.63 + 0.67 8.78 12.81 9.15 9.45 9.26 10.41 5.97N20 11.1 + 1.3 10.93 15.05 11.26 11.76 11.40 12.86 7.28NH3 26.6 + 1.7 11.57 55.92 22.35 23.68 25.91 28.64 23.84CH3NO2 41.6 + 4.1 13.33 94.73 34.52 46.53 42.65 48.68 41.72CH3F 12.3 + 3.3 11.32 58.95 23.10 27.41 27.14 30.15 25.33H20 b 9.13 64.11 23.41 25.31 28.88 32.93 28.36CH3N b 13.45 111.12 39.29 51.76 49.60 57.43 49.28ArMu + NO 3.21 ± 0.16 7.38 10.76 7.68 7.94 7.78 8.75 5.01NH3 b 10.18 49.22 19.67 20.84 22.80 25.21 20.99(C2H5)3N 8.6 + 4.0 15.82 27.13 17.21 19.43 17.39 19.43 12.79N2Mu + NO 1.46 + 0.14 8.02 11.70 8.35 8.63 8.46 9.51 5.45a Capture rate constants, in 10_b cm3 molec s’, calculated by the Langevin—Gioumousis—Stevenson method [110] (ignoring the dipole moment); by the equationof Moran and Hamill for a locked dipole [115]; by Su and Bowers’ ADO and AADOmethods [116,117]; from the paraineterized classical trajectory calculations of Chesnavich et al. [120]; by variational TST [120]; and by the quantum SACM method ofTroe [133].b No relaxation was observed.C Was not measured at room temperature.116mental rates at or below the capture limits. Figure 5.1 illustrates the agreement betweenthe results for dipolar molecules and the dipole capture theories, plotting k/kL vs. reducedtemperature. The solid symbols show the results for NeMu+ and the empty symbols arefor HeMu+. The results for high-dipole molecules are fairly widespread, extending fromnear the AADO line to below the Langevin line, while the low-dipole points (for N20and NO) are clustered near the common intersection at k = kL. Figure 5.1 and table 5.3show that the ADO predictions are closer, on average, to the experimental rates but thisassessment is unduly influenced by results that are clearly lower than their capture limits.The AADO and CT calculations give the best upper limits to the measured rates, with CTslightly better than AADO.Referring to tables 5.1 and 5.3, most of the results for both dipoles and non-dipolesare in fair to excellent agreement with the AADO or Langevin calculations respectively.Only the C2H4 + NeMu+ reaction is significantly faster than theory, and there are manyreactions that match or are marginally slower than the capture rates. However, a numberof the reactions are significantly slower than their capture limits: xenon, krypton, tetrafluorometharie, methyl fluoride, and difluoroethane with the HeMu+ and/or NeMu+ ions,triethylamine with ArMu, and nitric oxide with both ArMu and N2Mu; the reactionof krypton with NeMu+ is remarkably slow, and its reaction with HeMu+ was not seen.There is no general relationship between this shortfall and the reaction exothermicity(table 4.2), except for the Kr reaction which is particularly slow and is endothermic evenfor a bare jt. There might be a slight tendency for the endothermic (from the molecularion ground state) reactions to be slow (Xe, CF4,CH3F) but this ‘trend’ is violated by theendothermic N2O reactions occurring at the capture limit and by the exothermicC2H4Freaction which is even slower than the Langevin capture rate! This independence fromground-state exothermicity confirms the presence of sufficient excitation energy to allowthese reactions to proceed unhindered by a need for additional activation processes. Thisconclusion is also mandated by the majority of the studied reactions which proceed at1176.5.4.-3.kL2.1.0.2. 3. 4. 5. 6. 7.1//TRFigure 5.1 Plot of experimental results, expressed as k/kL vs. = ID/\/2akT,for HeMu+ and NeMu+ reacting with various dipoles at various temperatures, superimposed on theoretical curves for various theories of ion—molecule capture. The neutralreactants are identified by the symbol shapes (see legend); empty symbols are shown forHeMu+ and solid symbols for NeMu+. The theoretical curves are: a) locked dipole [115];b) Barker and Ridge average energy treatment [119]; c) variational transition state theory [120]; d) parameterized trajectory calculations [118]; e) AADO theory [117]; f) ADOtheory [116,117]; g) Langevin—Gioumousis—Stevenson [110]. The classical trajectory andAADO lines (d,e) appear to give the best upper limit to the reaction rates. Most neutralsreact at near this capture limit, but CH3F and C2H4F react considerably more slowly.0. 1.118their collision (capture) rates.The fact that all the reactions seen for ArMu+ and N2M11+ are relatively slow raisesthe possibility that the reacting ions are clustered with additional Ar or N2, e.g., Ar2Muor N4Mu+, which give a lower collision rate due to their greater masses. Such clusters are well known for the corresponding H ions [64,149,170,171] as well as for the unprotonated ions [26,145,172—177]. It is clear that clustering was not significant for theHeMu+ and NeMu+ ions because many of the neutrals reacted at the expected capturerate, but clusters might be more prevalent for Ar and N2 than for unpolarizable He and Ne,as supported by the observation that the termolecular formation rate of Ar2H+ is threetimes the rate of He2formation [172] (although it could also be argued that a factor of 3is not enough to make a major difference). The stability of Ar2Mu+ might also providean explanation of why no reaction was seen for (CH3)4Si in argon, where charge transferis exothermic from the ground state of ArMu+. Such cluster ions cannot totally accountfor the slow rates in Ar and N2 though even with large clusters, the reduced mass ofthe ion—neutral pair is not increased enough to give rates as low as seen, especially forNO in N2 where the greatest decrease in capture rate expected from ion clustering is afactor of 1.4 whereas kAADO/kexp = 5.9. Thus, the differences cannot be due to heavierions undergoing capture; instead, when kexp falls below the predicted rate, the reactionis not capture limited.A remote possibility for the low reaction rates is that the simplifications (pointcharge, etc.) necessary for the capture predictions are too extensive for those species.The actual capture rate could be reduced due to steric repulsion or other ‘chemical’ interactions which could extend beyond the capture radius of a large molecule. While thiscould conceivably apply to the larger molecules like C2H4F it is untenable for Xe and Kr,and the muonated (protonated) rare gases are excellent approximations to point-chargeions—the combination of small closed-shell ions and neutral atoms (or small molecules)is optimum for having strict separation of capture and ‘chemical’ interactions. Another119unlikely explanation for reaction rates below the capture limit is that the reactions areactivation limited rather than collision limited. The independence of reaction rate fromendothermicity noted above discredits this supposition, as do the temperature dependences to be discussed in section 5.7.A different explanation for the slow-reaction cases may be found in resonant chargetransfer and Franck—Condon overlaps [130,178,179]. The dissociative charge-transfer reaction (4.2) can be represented as two half-reactions [180]:X —f X + e (ionization) (5.1)MMu + e —+ M + Mu (dissoc. recombiriation) (5.2)the direct ionization of the neutral X, and the dissociative recombination (neutralization)of the MMu+ ion. For the overall charge transfer to be resonant, the energetics of thehalf-reactions must cancel, but resonance is not expected to be important because the dissociating M + Mu provides a continuum of available states. On the other hand, the ratesof each half-reaction could be heavily influenced by the Franck—Condon overlap betweenthe initial and final states. Each half will be considered in turn; first the dissociativerecombination, then the ionization.The potentials for HeMu and NeMu have their minima at a distance well withinthe repulsive region of the dissociative He + Mu and Ne + Mu potentials (see figure 1.1),so for a (vertical) electron-jump transition, the overall reaction is less exothermic (ormore endothermic) than expected. The lost energy goes into translational motion of theHe (Ne) and Mu. This effect is less at greater internuclear separations, so the chargetransfer reaction may only be possible at the largest separation in the HeMu+ vibration.The result is a low transition probability, or Frarick—Condon factor. FC factors haveoften been cited to explain charge-transfer reaction rates [178,181—184], although usuallyfor transitions between two bound states. The FC effect is applicable to a ground state120ion or to a rovibrational excited state, whichever needs to be at the far end of its vibrational level for a vertical transition which is part of an overall exothermic reaction. Sincevibrational excitation not only increases the available energy but stretches the bond, excitation does double duty in promoting charge-transfer reactions, but since there was noobservable relationship between reaction endothermicity and rate, FC factors must havelittle importance in the dissociative recombination half of the charge-transfer reaction.Franck—Condon factors also apply to the ionization of the neutral molecule reactants, such as C2H4, CF4, CH3F, etc., but excluding the atomic reactants Xe and Kr.The slow reactions seen for the fluoro-alkanes might indicate low FC factors, reflectingunfavourable direct ionization. However, there is no measurable FC overlap between CF4and any rovibrational state of CF [144,185] (which is why the ionization potential ofCF4 is not accurately known), yet the charge-transfer reaction occurs for both HeMu+and NeMu, albeit more slowly than the Langevin prediction. Since there is no identification of products, it might be argued that the CF is produced with energy above itsdissociation limit, but the reaction to produce ground-state CF is already endothermic(i.e., it requires initial excitation) so there is little chance of producing excited products.(Note that the neutral reactants have the energy distribution of the ambient temperature.) Since the observed reaction rate is within a factor of two of the Langevin rate,the FC overlap (or lack thereof) must not be very important. This is the situation formany other ion reactions [186—190], usually indicative of transient complex formation asopposed to long-range electron jumps, although FC factors are sometimes unimportanteven for long-range direct reactions [186].The Franck—Condon effect operates on the unperturbed reactants, and requires aninstantaneous transition to products; but is not applicable when there is a slow (adiabatic) transformation of a capture complex from reactants to products, or if the complexdistorts the reactants sufficiently. Since neither the neutralization of the muonated ionnor the ionization of the reactive neutral (especially Xe and CF4) appear to be controlled121by FC overlaps, the observed charge-transfer reactions must be predominantly mediatedby ion—molecule capture. This is obvious for the many cases that proceed with rates ator near the capture limit, but, with the arguments given above, now seems to be the caseeven for the slow reactions. The explanation for these cases is more likely found withinthe capture mechanism involving complex formation, stabilization, and/or breakup.Further support for the capture mechanism is the observation of both charge transferand muon transfer. If charge transfer occurred by long-range electron jumps, it wouldtend to prohibit muon transfer. Instead, charge exchange seems to occur at the shortranges where muon transfer is also possible.5.3 Unreactive NeutralsIn the previous chapter, table 4.2 gave a succinct summary of which ion/molecule combinations showed no reactivity. To it may be added the non-reactive combinations ofammonia, triethylamine or nitric oxide in hydrogen; ammonia or nitric oxide in ethane;and ethylene, carbon monoxide, or oxygen in nitrogen. That is not to say that k = 0, oreven that ke + kD = 0 for these reactants, but rather that ke < kD, possibly with ke = 0;see eqs. (4.12) and (4.34). Although charge exchange (ke), quenching (kq), and other (kD)reactions contribute to the signal’s relaxation rate, it is essential that charge exchangeoccurs if any relaxation is to be observed, for it is this process which is responsible forthe loss of spin coherence and hence muon depolarization. As revealed in table 4.2 andthe accompanying text, the energetics of charge transfer fall into three broad categories,with unreactive combinations in each.Charge transfer is endothermic for H2, CO, and Kr even with a bare so no depolarization was expected for these, and none was observed except for Kr + NeMu+, andthat reaction was very slow.’ It is tempting to explain this one reaction in terms of Xe‘ Looking at it another way, the NeMu + Kr reaction is remarkably fast given thatthe rate of the endothermic Mu formation reaction should be zero.122impurity in the Kr, but measurements in both He and Ne were made successively withthe same Kr, and no reaction was seen in He, so the relaxation must really be due to theKr + NeMu+ reaction. Except for this anomaly, the lack of charge-transfer reactions for112, CO, and Kr meets expectations. Note that the muon-transfer reaction is exothermicin all cases, even the combination of H2 + ArMu+, so muon transfer likely proceeds evenwhen there is no charge transfer to cause depolarization.For the more easily ionizable neutral reactants, charge transfer is expected for abare , but it is still endothermic for a ground state molecular ion. Yet charge transferwas seen for a number of such neutral species, and this was interpreted in section 4.3 asan indication that the molecular ion reacts from a rovibrationally excited state. However,not all such neutrals gave relaxation; CH3N, H20, and CH4 showed no reaction withHeMu+ or NeMu+, and Xe, 02, and NH3 gave none with ArMu+. In the latter case, thisprobably indicates that ArMu is in its ground state, as nothing reacted with ArMuexcept triethylamine and nitric oxide, for which charge transfer is exothermic from theArMu+ ground state. This is to be expected because Ar is a much better quencher ofions than either He or Ne [79,153,154]. The non-reactions with the He and Ne ions areless easy to explain because of the many similar reactions that were observed. It doesnot seem reasonable that H20 and CH4 would be excellent quenchers of (NeMu+)* and(HeMuj* while NH3 is not. The literature on collisional quenching of molecular ionvibrational excited states indicates that these particular molecules can be expected toexhibit wide variations in quenching rates; e.g., relative to NH3 and C2H4,both H20 andCR4 are an order of magnitude less efficient in quenching (NOj* [154,155] but they areboth relatively efficient at quenching (02j* [156], as is CH4 in quenching (ArHj* [191].In the absence of any evidence for superlative quenching by CH3N, 1120, and CH4,another explanation for their non-reactivity must be sought.Quenching should not even be considered for the third class of reactants: those forwhich charge transfer is exothermic even for a ground state molecular ion. Ethane showed123no reaction with HeMu+ or NeMu+ although charge transfer is exothermic, and the sameis true for (CH3)4Si (not) reacting with ArMu+. For both these exothermic cases and themildly endothermic cases above, charge transfer has somehow been suppressed relative tomuon transfer.Are the cross sections for charge transfer in the case of X = CH4,C2H6,CH3N,and H20 likely to be appreciably smaller than those of the other reactants investigated?There are no equivalent measurements on NeH+ or HeH+ to compare with, althoughcharge transfer (often accompanied by fragmentation) has been seen with a variety ofother ions [57,147,148,192—196] so it is unlikely to be something inherent to those particular molecules. Near thermal energies, one may expect the total cross sections forcharge neutralization for a bare muon to be comparable to those for the proton [44,86]The measured proton cross sections [197] give no indication, e.g., that u(CH4) .< u(NH3);indeed, if anything, the reverse may be the case, although the large uncertainties (factorsof 10!) in the low energy proton cross sections should be kept in mind.The present measurements of the total diamagnetic amplitudes give some indication of the epithermal charge exchange cross sections for with the neutral molecules.The trends in total amplitudes were presented in section 4.10, with the results listed intable 4.8. The parameter 3 is an indication of the relative efficiencies of muon thermalization and molecular ion formation by the moderator vs. muonium formation by thereactant, so a high value for implies relatively inefficient epithermal charge exchange,and vice versa. Particularly high values for were measured for Kr and CO in both Heand Ne, a finding which meets expectations based on the high ionization potentials ofthose neutrals, and which is also reflected in the lack of thermal charge-transfer reactions(with generally no relaxation seen). On the other hand, the other non-reactive molecules,CR4, C2H6, CH3N, and H2O, reveal no particular trend in ; in fact, CH3N gives aparticularly low value for /3, indicating a large epithermal charge exchange cross section.There seems to be no established trend in the ion—molecule literature that proton124transfer from protonated ions (including the protonated rare gases) to CH4,C2H6,or H20is anomalously fast [25,26,147,148,191,198], though there is one measurement of enhancedproton transfer for Ht + H20 [199]. Proton transfer of ArH with CH4, for example, isfairly slow [198]. Although proton transfer for these molecules is usually seen without anycharge transfer, the same is true for most other molecules, so that does not necessarilyimply a predominance of the muon-transfer reaction. If there is any correlation betweenproton affinity and proton (muon) transfer rate constants [25,195], one might expectNH3, with a proton affinity of 9eV [22], the largest for the reactants sampled (except for(C2H5)3N), to exhibit the fastest muon transfer (k11 > ke), contrary to observation.Although there seems to be no indication of enhanced proton transfer to CH4,C2H6,CH3N, and H20, there is a possibility of enhanced muon transfer due to quantumtunnelling. Tunnelling has been shown to be very important in studies of muonium reactivity [29—31], with isotope effects (kMU/kH) as high as 40 [30]. If there is a propensity forthe to tunnel through a barrier to internal rearrangement of the complex, then muontransfer could be greatly enhanced at the expense of charge transfer, and no relaxationwould be seen. This type of tunnelling has no precedent in conventional measurements,although hydrogen (H and H2) tunnelling through the rotational barrier has been implicated in some fragmentation reactions following ion—molecule association [32—35]. Thiseffect probably favours the emission of Mu from the capture complex; i.e., it promotesthe dissociative charge-transfer reaction rather than the muon-transfer reaction! Perhapssuch Mu tunnelling contributes to the general predominance of charge transfer for thereactions studied, and it is somehow suppressed in the non-reactive cases. The calculated potential [200] for triplet H has three minima, and tunnelling between them isan important process. Similar barriers for intra-complex rearrangement leading to muontransfer could be particularly narrow for CH4, C2H6, CH3N, and H20, in which casemuon transfer could be selectively enhanced for these molecules.Other means of enhancing muon transfer at the expense of charge transfer are energy125dispersal and fragmentation of the muon-transfer product. Since muon transfer is quiteexothermic for all the reactants studied, there might be a problem with energy disposalfor small molecules, hindering this channel. Large complexes like NeMuC2H disperseexcitation energy among many vibrational modes, making it less likely to be concentratedfor breaking the bond to Mu. Also, proton transfer to C2H6 is immediately followed byH2 elimination from (C2H)*, which is not itself observed [25,201] and the same thingundoubtedly happens for Mu. With fragmentation into such diamagnetic products asC2H4M11+ and HMu, muon transfer could proceed without any back-dissociation as mightoccur for XeMu+. Fragmentation reactions are expected to occur, but if energy disposalis the real limitation on muon transfer, it is not clear why charge transfer was observedfor other large molecules like C2H4F,(CH3)45i, and CH3NO2.Returning to table 4.3, it shows that the highest measured value for kD/ke (‘k,jke’)was 2.3 (CH3F in He, followed closely by Kr in Ne). As long as moderator quenchingis relatively slow (kq[M] is small), ratios as high as kD/ke 5 should give measurablerelaxation; higher than this, the relaxing component might well be undetectable. Thus,the muon-transfer reaction (or quenching by the neutral) would need only moderate enhancement for there to be no reaction seen.5.4 Ternary Mixtures: Monitor Gas MeasurementsIn order to see that there was some reaction with the apparently non-reactive neutrals,and to determine if their muon-transfer rates were enhanced beyond the capture rate,measurements were made with additional reactive gas (i.e., one that does undergo chargeexchange). The extra reactant gives a visible relaxation which facilitates measurementof muon-transfer rates. This is the monitor ion method, typically used to measure thequenching rate of excited molecular ions [79,153—157,202—204]; here, though, the appearance of the monitor ion is not measured, but the disappearance of the reactant ion.126Assuming there is no interference between the two neutrals X and Y, the simplemodel (4.12) is applicable, and the experimental reaction rate is the total of all rates:= (k + k)[X1 + (1 + k)[Y] + kq[M] (5.3)and the relative amplitudes are given by— k[X] + k[Y] + kq[M]- k[X] + k[Y]When the monitor gas concentration [Y} is kept constant, the relaxation rate is fitted by astraight line having the slope k = + k, and the intercept (k’ + k)[Yj + kq[M]. Therelative amplitudes cannot be fitted linearly, as they were for binary mixtures, but thereis no difficulty in fitting them to the three parameters k[Y]/k, (k[Y] + kq[M])/k, andk/k. (The actual rate constants cannot be determined from eq. (5.4) alone, and theratio ke/kD was chosen for fitting because kD/ke tends to infinity for reactants such as0114.) Plots showing these fits to the relaxations and amplitudes (Af/AS) for Y = NH3and X = C2H6 and H20 are given in figures 5.2 and 5.3. Measurements were also madefor X = OH4,H20, and NH3 with Y = Xe; as summarized in table 5.4.Two different monitor gases were chosen: xenon and ammonia. Xe has the advantageof being inert, but might suffer from complications, especially due to quenching, whileNH3 might be susceptible to clustering with H20. The measurement ofH20+NeMu+ wasperformed with both monitors, during different run periods, to check for interferences,and the two results were quite different (table 5.4), with the rate constant measured forthe H20/NH3mixture agreeing quite well with the AADO prediction, and the H20/Xemixture giving an anomalously low rate. If the interfering side reactionNH3 + H20 — NH3•H20 (5.5)was occurring, the observed rate constant would be expected to be reduced for NH3 dueto the reduced concentration of free NH3 and 1120. Instead, it is the reaction measuredwith the Xe spectator that is anomalously slow, and there is no evidence for clustering.127C2H6 + HeMu + NH30.0 2.0 4.0 6.0 8.0 10.0 12.04.0 I I3.00.0 2.0 4.0 6.0 8.0 10.0 12.014 —3[C2H6] / 10 molec cmFigure 5.2 Relaxation rates (top) and relative amplitudes (bottom) for the reactionof C2H6 with HeMu+ in the presence of 5.08 x 1014 rnoleccm3of NH3. The slope of )gives lc = 17.4 ± 2.6 x 10_ID cm3molec s1, and the high-concentration asymptote ofAf/AS is ke/kD = 0.15 ± 0.11. Note that Af/AS is plotted here, whereas A/Af is shownin figures 4.7 and 6.2.128H20 + NeMu + NH36.0 I I0 3 6 9 12 15 18[H20] / 10 molec cmFigure 5.3 Relaxation rates (top) and relative amplitudes (bottom) for the reactionof H20 + NeMu, with 6.12 x 10’ rnoleccm3of added NH3 monitor gas. The fits giveICC = 23.7+2.8x 10’°cmmolecs ,and ke/kD = 0.23+0.09 (kD/ke = 4.4+1.6). Notethat the plot of the amplitudes shows Af/A, which is the reciprocal of what is plotted infigure 4.7.129Table 5.4 Results for Ternary Mixtures Employing a Reactive Monitor GasReagent (X) CH4 C2H6 H20 H20 NH3Ion HeMu+ HeMu+ NeMu+ NeMu+ NeMu+Moderator He He Ne Ne NePressure/torr 1500 1500 800 800 800Monitor (Y) Xe NH3 NH3 Xe Xeyja 11.1 5.08 6.12 10.0 10.0b 22.8 + 8.0 17.4 + 2.6 23.7 ± 2.8 13.4 + 1.9 17.7 + 1.0kL, kAADO 20.85 26.04 25.31 25.31 23.68k’[Y]+kq[M] c 2.51 ± 0.19 2.056 + 0.078 1.275 + 0.078 0.880 ± 0.023 0.869 ± 0.028k/k 0d 0.15±0.11 0.23+0.09 0d 2.7+0.9k/k 00d 6.5+4.8 4.4±1.6 Dod 0.37±0.13k/k 0.91 + 0.19 0.70 + 0.13 1.16 ± 0.17 0.255 + 0.013 0.51 ± 0.238.6+2.6 21.2+4.1 22.4±3.7 1.39+0.10 2.8±1.3a The concentration of the monitor gas, in iO’4 moleccm3.Total rate constant (k = ke + kD) for the reaction of the ion with the reagent gas,in 10_lU cm3 molec’ s1. For these reagents (except NH3), ke < kD 50 k lCD =k + k[M] k.C The intercept of vs. [X], in representing the reaction rate with the monitor gasat its fixed concentration [Yj plus a small contribution by moderator quenching.d In two cases the ratio ke/kD was fixed to zero: For methane, the parameter was completely undetermined by the data and so ke/kD = 0 was chosen based on the absenceof any relaxation for CH4 + HeMut For water vapor, ke/kD went to a slightly negativevalue in a free fit so it was fixed at zero for a refit.k values calculated from the row above and the values of k” listed in table 4.4.130All the xenon ternary mixture reactions are slow, including the NH3 + NeMu+ reaction with a Xe monitor whose kexp came out much lower than the measurement for NH3alone (table 4.1). The low rates can be regarded either as a spurious artifact, since themeasurements were made consecutively, or as an effect of Xe itself. The anomalously lowmeasurements were also performed consecutively with a measurement of the Xe + NeMu+rate (5.35) which agreed with earlier determinations, supporting the validity of those lowvalues. It was already apparent (section 5.2) that Xe reacts at only half the expectedcapture rate (kexp vs. kL), and, like all the slow reactions, this is likely due to a morecomplex reaction mechanism than the simple one chosen, eq. (4.12).Although the total rate constant determined for NH3+ NeMu in the presence of Xewas low, the relative contribution of each reaction channel, kD/ke, agrees well with theearlier determinations (table 4.3), lending support to the general validity of the ternarymixture measurements, and indicating that Xe does not interfere with the NH3 reactionmechanism. Instead, it is likely that NH3 does interfere with xenon’s reaction. Themeasurements 1120 and NH3 with a Xe monitor are thus valid, but the resulting kexpvalues are not appropriate for pure H20 and NH3.Determinations of kD/ke for H20, CH4, and C2H6 meet expectations that kD >> ke,although the value of 4.4 seen for H20 + NH3 + NeMu+ seems low enough that somesmall relaxing component should have been seen for the pure H20 determination. Thetwo measurements that gave ke/kD > 0 were taken when the high value for NO + ArMu+was taken (see section 4.2), which might have been due to leaks in the apparatus. If thatis true, the rates for water and ethane may be inflated, especially Ice. However, given thatkD/ke was still high, this effect must have been small, and is unlikely to have affected thetotal (capture) rates appreciably.On the whole, the results from ternary mixtures are quite believable, giving rates ingood agreement with theoretical capture rates when monitored by NH3, but giving overallrates lower than the capture limits when measured in the presence of Xe. Methane is the131exception in that its reaction rate agrees with Langevin theory although it was measuredin a xenon/helium mixture.5.5 Comparison with Protonated Inert Gas ResultsAs noted earlier, charge exchange is rarely seen in studies of the protonated ions; protontransfer is the overwhelmingly dominant reaction channel [16,24,25,79,139,145—149]. Thepresent study of muonated ions indicates that both electron and muon (proton) transferare ubiquitous, with rate constants ke and k,L such that ke + k = kexp, identified as thecapture rate constant k in table 4.4. These results are compared with the correspondingprotonated ion reactions in table 5.5, though there are few such studies for comparison;the ArH+ + H2 reaction seems to be the favorite and occupies nearly half of this table.Only the tandem ICR work of Smith and Futrell [191] has shown both charge exchangeand proton transfer but, unfortunately, only their results for C2H4, reacting with HeH+and NeH+, are comparable with reaction rates measured for this thesis.The great pressure difference between the present experiments and the ICR [191] measurements of C2H4+ HeH+ and NeH+ (1 atm vs. iO torr) would suggest that differentresults might be seen. Instead, the agreement is exemplary: both the proton/muon-transfer rates and the charge-transfer rates are in agreement, and both experiments measure reactions of vibrationally excited ions. The Smith and Futrell ICR results listed intable 5.5 were determined in both the limits of zero moderator collisions, corresponding toexcited ions, and after many collisions, corresponding to ground-state ions; it is the formerthat best match the reaction rates measured for (HeMuj* and (NeMu+)*. Interestingly,there is still a contribution from charge transfer for apparently ground-state HeH+ andNeH+, whereas all other protonated ion studies detected only proton transfer. Chargetransfer was certainly favored by the excitation, but the total reaction rates were essentially unchanged, as is appropriate for capture-limited reactions. The same apparentlyapplies to the muonated ions as well as the protonated ions.132Table 5.5Comparison of Present Results with Those for Protonated and Deuterated Inert GasesMu results H, D resultsNeutralReactants ktiieoa kexp ke k kexp ke k refHeH + H2 18.1 b $3 0.2 18.3 ± 0.6 0. 18.3 205HeH + Kr 18.7 b 0.2 12. + 2. 0. 12. 25HeH+O2 15.4 12c 116d 0.3 11. +2. 0. 11. 25HeH + C2H6 30.1 17.4 + 2.6e 0. 17. 21. + 4. 0. 21. 25HeH + C2H4 25.5 25.0 ± l.&’ 14.2 10.7 28. ± 5. 15. 13. 19128. ±5. 7. 21. h 191NeH + H2 15.5 b 0.2 0.2 0. 0.2 171NeH + C2H4 14.1 18.6 + 3.5 8.2 10.4 18. + 4. 8. 10. g 19118. ± 4. 4. 14. h 191ArH+ H2 15.2 b 0.2 8.9 0. 8.9 145ArH+ 112 3.4 0. 3.4 191ArH + H2 8.0 + 2.4 0. 8.0 198ArD + H2 8.8 0. 8.8 145ArD + H2 4.5 0. 3.4 191ArD + NH3 20.8 b 0.2 21.4 ± 3.2 6. 15. g 191ArH+ 02 7.0 b 0.2 4.1 0. 4.1 146ArH(D)+ 02 6.0 + 1.8 0. 6.0 198N2H + NO 8.6 1.46 + 0.14 1•4d 0. 3.4 0. 3.4 203a All rate constants are in units of 10_b cm3molec’ 5_i; ktheory is the Langevin or AADOprediction for the MMu+ ion. Theory values for HeH+ are ‘—10% lower than HeMu+due to the mass difference; other theory values independent of H/D/Mu.b No relaxation seen, so the capture and muon-transfer rates are ill-defined and thecharge-transfer reaction is very slow (ke 0.2).C The HeMu+ + 02 reaction was not measured, but estimated by scaling the NeMu+result according to the mass dependence of eq. (3.7).d Both charge transfer and depolarization of NOMu+ and O2Mu+ may contribute to therelaxation.e Measured in the presence of NH3 monitor gas, see table 5.4.Measured at 398 K; all other measurements were made at room temperature.g Results of Smith and Futrell [191], using the product distributions in the limit of zerocollisions, giving the (MHj* reactivity.h The same, but measured after many quenching collisions, corresponding to ground-statereactants.133Smith and Futrell also measured reactions of ArH+ under similar conditions [191,198]and saw some charge transfer with NH3 before quenching of (ArH+)*, whereas no reactionwas seen for ArMu+. This is not to say that there is no reaction at all—muon transferundoubtedly takes place, but in the absence of any depolarization from Mu formation,the reaction remains undetectable. This difference, after the agreement for He and Neions, indicates that ArMu is quickly quenched to its ground state by the ‘—‘ 1 atm argonbath. Note that the only reactions observed for ArMu+ were with nitric oxide and tnethylamine, for which charge transfer is exothermic from the ground state. These resultsagree with the usual finding that N2 and Ar de-excite molecular ions much better thando He or Ne [16,79,153,154,206—208].Villinger, Fiitrell and co-workers [198] had similar results for the reaction of (ArH+)*with 02— some charge transfer before de-excitation of the ion, and a predominance ofproton (deuteron) transfer—while Lindinger et al. [146] saw only proton transfer whoserate increased with vibrational excitation. ArMu+ gave no visible reaction with oxygen,but no charge transfer was expected, based on the energetics for ground-state ArMu+, inseemingly good agreement with the H-ion results. The problem with this is that O2Hhas a diradical triplet electronic ground state [152,209] in which the spin would bedephased and depolarized in a transverse magnetic field, even in the absence of Mu formation. Might the effect of excitation observed by Lindinger be even stronger for ArMu+;so much so that there is no muon transfer for ground-state ArMu+’? It is a possibility,as the proton transfer is only 0.55 eV exotheninic and energetics probably favor protonover muon transfer: A likely zero-point correction for O2Mu+ is 0.39 eV, based on thecalculated 02H vibrations [209], whereas the ZPE shift for ArMu is 0.27 eV [78], whichmake the ArMu reaction 0.12 eV less exothermic than for ArH (0.43 eV vs. 0.55 eV).This should still be enough for the reaction to proceed.Rather than positing that transfer is non-existent for ArMu+, the result could beattributed to the formation of electronically excited O2Mu+. The first three electronic134excited states of O2H are spin-singlet, 0.26, 1.28, and 3.31 eV [152] above the tripletground state, and muon transfer from ground-state ArH+ to the lowest of these is stillexothermic by 0.43 — 0.26 = 0.17 eV.2 The lack of depolarization would require thatsinglet O2Mu+ is formed almost exclusively. Selective population of product states isa common occurrence, but typically only for resonant reactions [187,210]. Resonant ttransfer is a possibility because the remaining 0.17 eV exothermicity could easily be usedup by forming rotationally excited O2Mut (Note that 0.17 eV is much less than theexpected ( 1 eV) vibrational spacing.)An alternative explanation was mentioned in section 5.2: the possibility that theArMu+ might form clusters Ar71Mu+. J particular, the Ar2H+ ion is 0.51 eV more stablethan ArH [64,170], making the reactionAr2H +02 —÷ O2H + 2Ar (5.6)exothermic by just 0.04 eV (all species in their ground states) and the Mu analog endothermic by 0.08 eV! This is more a case of a near-resonant reaction rather than an endothermic one, so it is not clear that this reaction would prevent the formation of O2Mu+and its subsequent depolarization; it might even promote it. The presence of ArnMu+was also implied by the lack of depolarization for (CH3)4Si + Ar mixtures, although the(CH3)4Si+ ArMu+ charge exchange reaction is more exothermic than 02 + ArMu+ muontransfer. It is a pity that there are no good comparisons of ArH+/ArMu+ reaction ratesto prove (or disprove) that the ionic reactant is really ArMu+. The comparisons for theHe and Ne ions demonstrate that no clustering takes place in those moderators, giving asimilar expectation for Ar. Nevertheless, clustering seems a more viable explanation forthe lack of depolarization in ArMu+ + 02 than does the formation of excited O2Mu+.2 presuming that the 02Mu ZPE is the same for each state; this is likely true forthe lowest singlet state (11A’) whose potential energy curve has much the same shapeas the ground (13A”) state [152].135The other entry for 02 in table 5.5, due to Bohme and co-workers [25], gives theproton-transfer rate constant for 02 + HeH+. Unfortunately, this combination slippedthrough the cracks of the present experimental program, which has measured only thereaction of 02 + NeMu+, so the value of kexp = 12 for the 02 + HeMu+ reaction had to beestimated from the neon result based on the difference in reduced mass. Nevertheless, thisestimate agrees very well with the HeH+ result of 11±2 x 10_b cm3molec’s1, and bothare slightly below the Langevin prediction. Yet there is a striking difference between themeasurements: Bohme observed only proton transfer while we saw apparently no muontransfer, only charge exchange. This appearance may be caused by spin precession anddepolarization of triplet O2Mu+ formed by muon transfer, but there is reason to believethat this is not the whole story.As discussed above, formation of O2Mu+ in Ar gave no depolarization, with thepossibility of excitation in the muonated oxygen. Muon transfer from NeMu+ is moreexothermic than from ArMu+ and so should give more excited singlet O2Mu+. It is hardto believe that there would be as little singlet product as indicated by the apparent kjke.Instead, there is probably little muon transfer taking place, with a predominance of chargeexchange. Some part of the difference from Bohrne’s results may be due to depolarizationof O2Mu+ after muon transfer, and also to differences between the HeMu+ and NeMu+ions, but the major difference is probably in the excitation—the muon ion results involveexcited NeMu+ while the proton ion results are for ground state ions, for which the chargeexchange reaction is endothermic.Another point of comparison between this work and that of Bohme, Mackay, &Schiff [25] is the HeH+ + C2H6 reaction. The two measurements agree quite well in therate constant and in detecting only proton (muon) transfer, though the C2H productwas not observed because of its ral)id fragmentation into C2Ht + H2. This is probably a feature of the it-transfer reaction as well. The Langevin rate over-estimates bothmeasurements significantly.136There are several measurements of protonated and deuterated ions reacting with H2by proton (deuteron) transfer, but none of these were visible for the muonated inert gasions.The N2Mu+ reaction with NO was the only case where there is significant disagreement with literature values for total reaction rate; the Mu rate is only half of the H ratemeasured by Rakshit [203], which is itself less than half the AADO capture rate. Like theoxygen reactions, both Mu and NOMu+ formation may contribute to the total reactionrate. The N2H+ ion reacts purely by proton transfer.The impressive agreement, insofar as comparisons are possible, between the reactionkinetics of the muonated, protonated, and deuterated ions reveals a total lack of isotopicsensitivity; surprising when viewed in terms of the very large effects seen for reactionsof neutral Mu [29—31]. Some isotope effect on the proton/muon-transfer rate had beenexpected, and even charge transfer could be affected. However, any differences observedare more probably a result of differences in excitation; the muon ion results involve excited NeMu+ while the proton ion results are for ground state ions, for which the chargeexchange reaction is endothermic. The excellent agreement between the present workand the proton ion data, considering the vastly different pressure regimes utilized, indicates that total pressure plays a negligible role in ion—molecule reactivity, even whenion excitation is important, in sharp contrast to other measurements of excited ion reactivity [201,205,211]. What makes this even more remarkable is the fact that the highpressure Mu ion measurements reveal more ion excitation than is evident in the lowpressure H ion results.While these comparisons are illuminating, the relative lack of data for the corresponding reactions of the HeH+, NeH+, and ArH+ ions frustrates the potentially important broadcomparisons that could otherwise l)e made with the present iSR results. It is importantto emphasize, in this context, that the jiSR measurements have considerably expandedthe data base of ion—molecule reactions undergone by these simple point-charge ions.1375.6 Unreactive IonsIn the investigations of molecular moderators, and therefore polyatomic molecular ions,very little (charge transfer) reactivity was seen. No signal relaxation was seen for ammonia, triethylamine or nitric oxide in hydrogen; none for ammonia or nitric oxide in ethane;and none for C2H4, CO, or 02 in nitrogen, although NO did react with N2Mu.It is not at all surprising that there was no relaxation in ethane moderator, evenwith nitric oxide reactant. The binding energy of C2H6Mu is not known exactly, butthe proton affinity of C2H6 6 eV [22,144]. Assuming a zero-point energy correctionfor C2H6Mu+ of 0.3 eV, the charge-transfer reaction with NO would still be endothermic by 1.4 eV. The ethane moderator is undoubtedly an extremely efficient quencher of(C2H6Muj*, it quenches (NOj* very well [155] and would benefit from its similaritywith (C2H6Mu+)*, which generally enhances quenching efficiency [153,154,157], so thereshould be very little excitation of the inuonated ethane. The supposed zero-point correction of 0.3 eV is a very generous estimate; the true value is probably considerablyless because C2H very weakly bound, being prone to fragment into C2Ht + H2 [212].In fact, this undoubtedly happens in the present studies, placing the Mu in either theeven-more-stableC2H4Mu+ ion or the diamagnetic molecule MuH, neither of which wouldreact with even nitric oxide.These considerations may not come into play because it is likely that no molecular ionis formed! The diamagnetic signal in low pressure C2H6 is consistent with the molecularproducts of muonium hot atom reactions which occur during thermalization [38,90].There are appareit contributions from MuH produced by H-atom abstraction at 10 eVkinetic energy, and fromC2H5Mu formed by Mu substitution occurring near 5eV, followedby collisional stabilization of the (C2H5Mu)* [38]. Such reactions occur too quickly tobe observed directly by tSR, but are reflected in the ‘initial’ (after Mu thermalization)amplitudes of Mu and diamagnetic signals; there has been much study of hot-Mu chem138istry [38,89,90]. The formation of the molecular ion was not absolutely ruled out in thosestudies, but its existence was deemed improbable. Even if the muonated ethane ionis formed initially, and it doesn’t fragment, it may react by proton transfer with otherethane molecules according toC2H6Mu + C2H6 —* C2H5Mu + C2H. (5.7)It is not certain that this reaction proceeds, as only a detailed calculation of the energetics could reveal the small differences in stabilities; however, the equivalent reaction forH2Mu+ is calculated to be exothermic [81], and the ethane reaction is likely to be as well.With all these processes working against it, it is hardly surprising that no C2H6Mu+ wasseen.This brings us to the other molecular moderator that gave no relaxation of the signal: H2. The binding energy of 112 + Mu has been calculated [81,144] as D0 = 4.142 eV,so although charge transfer with NH3 is endothermic by 0.77 eV, it is exothermic for NOand (C2H6)3Nby 0.13 and 2.3 eV respectively. But no reaction was seen for any of thesethree, not even a muon-transfer reaction with NO.It is almost certain that the diamagnetic signal in H2 is due to MuH rather thanH2Mu. The molecular ion might be formed initially, but the reactionH2Mu + H2 —* H + MuH (5.8)has been calculated [81] to be exothermic by 0.07 eV (7.0 kJ/mol), even though the Hhas a J = 1 ground state while H2Mu is J = 0, and so the Mu would be quickly shuttledinto Mull. However, the dominant source of Mull is likely to be the neutral exchangereactionMu +112 —* MuH + H, (5.9)again due to Mu hot atom chemistry. Thermally, this endothermic reaction is slow, butit has been well studied over the temperature range 470—840 K [82]. At many eV, it139should have a substantial cross section [213]. Furthermore, measurements of the diamagnetic fractions in H2 and D2 fit established notions of hot atom reactivity, includingthe Wolfgang—Estrup formalism [90,213,214]. These considerations point to the absenceof H2Mu+, and so explain the absence of observable molecular-ion reactions with H2.Epithermal Mu reactions with the noble gases and N2 are not really feasible.5.7 Temperature DependencesSeveral reactants were studied over a range of temperatures, from as low as 117 K up to445 K. The lowest attainable temperature was often limited by the vapor pressure of thereactant gas—when too low, it was impossible to introduce the vapor to the reactionvessel—thus, e.g., the lowest temperature attained for nitromethane was 223K. In fact,acetonitrile, acetaldehyde, and difluoroethane were chosen as reactants for their high vapor pressures relative to their dipole moments. The thermal homogeneity of the gas wasless than ±1 K, but the variation of T over time was larger, more like +5 K at the low10.08.0r6.0C’)1-2.00.00 10 20 30 4014 3[NH3] (10 molec/cm )Figure 5.4 The relaxation (reaction) rates for NH3 + NeMu+ vs. NH3 concentration at 445 K (o) and 179 K (A). The slopes give rate constants of 22.6 and27.0 x 10_b cm3molec’ s’ respectively.140temperatures. The experimental rate constants measured at the various temperatureswere given in tables 4.1 and 4.4. The variation of the rates with T were generally small,as shown by figure 5.4, which plots the relaxation rates measured at 179 K and 445 K forthe NH3 + NeMu reaction.According to the Locked Dipole, AADO, and other theories of ion—dipole capture,the rate constant should vary as i//, so linear fits of k vs. to the data wereperformed with the results listed in table 5.6. Figures 5.5—5.12 show the measured totalrate constants vs. i/\/, with the linear fits to the data plus the AADO and SACM (or Langevin) predictions. The AADO (and other) calculations deviate from being linear insofaras the locking “constant” C varies3 with temperature, but the variation is small over thetemperature ranges investigated, so the theory lines are linear in the range of the data.Linear extrapolation beyond this range accounts for intercepts visibly different from theLangevin values (figure 5.5 shows kAADO = 9.5 at T2 = 0 whereas kL = 11.6). Becauseof this difference, table 5.6 also lists the slopes and intercepts of the AADO calculation asdetermined by values at 200 and 400 K, thus facilitating comparison with the linear fitsof the experimental data (and also reducing computation).Some of the reactions are fitted well by capture theory: NeMu+ plus NH3,CH3NO2,and N20. Although the NH3 measurements show considerably less variation with temperature than the AADO and SACM calculations do, all three lines on figure 5.5 intersectin the midst of the data points, indicating good agreement. The experimental slope forthe N20 temperature dependence also appears to differ from the AADO prediction, but,given the uncertainties in the points, the difference is not really significant; and the AADOline does agree well with the points themselves. The corresponding SACM calculation fallsfar below the points, but one can have no confidence in SACM’s predictive ability for sucha weak dipole as N20: in the (lerivation of the SACM treatment it was assumed that theAlthough C is not constant with temperature, the term “locking constant” is assensible as “rate constant” or “equilibrium constant.”141Table 5.6Fits to Temperature Dependences Compared with Theoryexperiment AADONeutral (X) M slopea k(300)b slopea k(300)bXe Ne 3.1 ± 8.0 5.19 + 0.14c 0 11.2N20 Ne —56 + 52 12.99 ± 0.73 19 11.8NH3 Ne 158 + 45 24.54 ± 0.59 245 23.7CH3NO2 Ne 580 ± 400 34.3 + 2.6 610 46.5CH3F Ne —1:30 + 62 14.02 + 0.84 314 27.4CH3F He 550 + 110 31.1 + 2.1 584 51.0C2H4F He 640 ± 76 14.00 ± 0.81 823 68.3CH3HO He 1170 ± 290 41.0 + 2.8 903 73.6a —10 1/2 3 —1 —1The slope of k(T) vs. v 1/T, in 10 K cm molec s , from fitting the experimentalrate constants and the nearly-linear AADO predictions.The rate constant at 300 K, in 10_b cm3 molec’ s1 determined by the fit to theexperimental data or by the linearization of the AADO theory.The results for Xe are clearly fiat, as expected, so the average k is given for k(300)instead of the result from the linear fit. The theoretical k(300) listed is the Langevinrate.C,)00)0EI)E0o00.‘C0C,)()ci)0I..,E0000.01424030201000.00 0.02 0.04 0.06 0.08 0.10T112Figure 5.5 The experimental rate constants for NH3 + NeMu+ over the temperaturerange 179—445 K, plotted as i/Vt. The solid line is the fit to the data, the dashed lineis the AADO prediction, and the dot-dashed line is the SACM calculation. Although theslopes are somewhat different, all lines agree with the data.6045301500.00 0.02 0.04 0.06 0.08 0.10Figure 5.6 kexp for CH3NO2+ NeMu vs. i// for T in the range 223—406 K. Thedashed and dot-dashed lines are AADO and SACM predictions, respectively. The pointsfall only slightly below theory, although, given their scatter, it is somewhat fortuitousthat the fit matches the slopes of the theory lines so well.If)0G)aEE0000xU)U)()ci)0EE()000.U)90756045301500.00 0.02 0.04 0.06 0.08 0.10Figure 5.8 kexp vs. 1/v’, as above, but for the HeMu+ ion. The agreement withcapture theory is much better, though the data is significantly below the predictions.14350 I I40-30 -0.00 0.02 0.04 0.06 0.08 0.10T12Figure 5.7 kexp at various temperatures for the reaction CH3F + NeMu+. The solidline is a fit to the data and the dashed and dot-dashed lines are the AADO and SACMpredictions, which miss the data entirely.T112Figure 5.10C,,C-)U)0EI.,EC)000x-Cl,C-)a)0EW)E0000‘CC’As above, for C2H4F over the temperature range 148—4 06 K. This data1441008060402000.00 0.02 0.04 0.06 0.08 0.10T112Figure 5.9 The two values of kexp at different temperatures for theCH3HO+ eMu+reaction, compared with capture theory; the line types are the same as for preceding plots.The points fall well below the theory, but with a similar slope, giving an unphysicalk(oo) <0.1008060402000.00 0.02 0.04 0.06 0.08 0.10T12falls far below theory, but, again, with the same slope.4520 IU)8)I I I I0.00 0.02 0.04 0.06 0.08 0.10T112Figure 5.11 Results for N20 + NeMu at various temperatures. Although the experimental points decrease with decreasing temperature (increasing i//), the trend isprobably not significant, and the AADO predictions fit the data well. The SACM valuesare very low, but the SACM treatment is invalid for such a weak dipole.12.5 ICl)- 10.0EI, 75EC.)o I,500I I I0.00 0.02 0.04 0.06 0.08 0.10T112Figure 5.12 Experimental rate constants for Xe+ NeMu+ over the temperature range117—445 K, plotted as i/Vt. The line of small dashes is the fit to the points, whichare obviously independent of T; thus, the horizontal solid line is drawn at the average k = 5.19 x 10_b cm3molec1s. The high dashed line is the Langevin prediction,= 11.2.146permanent dipole dominated the polarizability. The agreement in the case of CH3NO2is impressive, especially for SACM; however, it should be noted that the parallel lines offigure 5.6 are fortuitous because the slope of the fit is very uncertain (table 5.6).For several other reactants, the situation with CH3NO2 is magnified—the trendswith temperature match theory, but the points are displaced to lower values. For theXe + NeMu+ reaction (figure 5.12), the data are impressively temperature-independent,as expected for non-polar Xe, but with rate constants only half the Langevin value. BothC2H4F and CH3HO reacting with HeMu give the predicted variations with temperature (slopes), but have negative intercepts! While a slight displacement to lower k valuesmight be due to polarizabilities being lower than the literature values, this could not givean unphysical negative k at high temperatures. Nor are the low values due to thermally-activated reactions, for if they were, they would have the reverse temperature dependence.Instead, some subtleties in the reaction mechanism are indicated.The reaction of CH3F with NeMu+ increases in rate at higher temperatures, unlikea capture process. The charge-transfer reaction is endothermic by 0.72 eV = 69 kJ/mol,but that is too high to believe the reaction is thermally activated, especially for sucha weak temperature dependence. Although there may be some small barrier to muontransfer within the capture complex, there would be more than enough energy availablein (NeMuj* to cross it without needing thermal excitation. Recalling the great effectNe moderator pressure had on this reaction ({kq + ks[M1}/ke in table 4.6), it is likely thatthe temperature dependence is a result of changes in moderator quenching of the capturecomplex, or some similar quenching mechanism.The quantum SACM calculations for the rate constants are included in figures 5.5—5.12 to see if they could fit low-temperature results better than the classical AADO calculations. Although the SACM lines do not overlap the AADO ones, they do run parallelfor all reactants except NH3; and they are truly linear over the range of temperaturesstudied. It could be argued that the measured points do, on average, lie closer to SACM147predictions than to the AADO, but the SACM calculations underestimate the effect of thepolarizability and the difference between SAC’M and AADO is mainly due to this, ratherthan to discrete rotational levels. Of the molecules studied, NH3 has the lowest momentof inertia and the widest rotational quantization and, indeed, is the only molecule forwhich the SACM calculation exceeds AADO within the temperature range of the data.The difference is slight, however, and both predictions fit the data well. For the reactionsstudied, capture is still essentially classical, even at the lowest temperatures investigated.Selecting the best classical treatment is more difficult, as many of the reaction ratesfall below all the capture predictions; these reactions are obviously not capture limited,even though the muonated rare gas ions are the molecular ions that most resemble apoint charge. The best upper limits on the observed reaction rates are provided by theVTST [120], AADO [117], or the parameterized trajectory [118] calculations.Chapter 6EXCITATION AND QUENCHINGThe energetics of the ion—molecule reactions studied are central to an understanding oftheir kinetics, and this topic has been considered in the discussions thus far, but onlyto a limited extent. The observation of several instances of endothermic charge transferled to the conclusion that the muonated rare gas ions HeMu+ and NeMu+ must have anexcess of energy, probably in the form of rovibrational excitation (see §4.3), while ArMu+probably reacts from its ground state, or even from an ArMu+ cluster.Since the data called for an unseen reaction between the moderator and the ions,quenching of the excited ions through collisions with the moderator gas was implicated.Excitation energy could also be lost to the dilute reagent, which may have quenchingefficiencies ranging to thousands of times higher than He or Ne [79,153—157), generallywith greater efficiency for complex molecules and those of similar structure to the ion.Quenching by the reagent is hard to distinguish experimentally from the muon-transferreaction, but not so for quenching by the moderator, which is manifest in many forms:Quenching rates were measured as zero-reagent-intercepts of the signal relaxation rate, asthe variation of the relative amplitudes with reagent concentration, and as variations inboth amplitudes and relaxation rates with changes in moderator density. The discussionin this chapter will focus on the details of the reaction energetics and on the variousmeasurements of quenching, including some measurements of quenching by argon notpresented yet.1481496.1 Molecular Ion Formation and Excitation StateAs described in chapter 1, muonated (and protonated) rare gas molecular ions are expected to form by the association of a bare muon (proton) with the appropriate gasatom at kinetic energies below 1 eV. This was substantiated by the results presented insection 4.10 indicating that association probably happens at a low enough energy to beaffected by the polarizabilities and dipole moments, and also below where most epithermalMu formation happens. Although some energy must be carried off by the moderator forthe association+ 1He M 1HeMu1+lNeMuJ(6.1)to occur, the low quenching efficiencies of He and Ne [16,79,153—157,206—208] and H2 aswell [153,204] allow substantial rovibrational excitation to remain. HeH and NeH haveboth been observed in excited states [71,191], although at much lower bath gas densitiesthan employed for these experiments.What is the minimum excitation needed to allow the Mu formation reactions thatwere observed? Table 4.2 shows that, except for Kr, which is dealt with in the next section, the most endothermic charge-transfer reactions observed were those of CF4, in bothHe and Ne, requiring 0.99 and “.i 1.25 eV of excitation respectively. These numbers areuncertain, though, as the ionization potential of CF4 had to be estimated; the next mostendothermic reactions, for N20, are not much different at 0.88 and 1.13 eV. From thecalculations of Fournier, Le Roy, and Lassier- Covers [75] (table 1.2) the necessary excitation corresponds to (v, J) = (2,0), (1,2), or (0,6) for HeMu + N20; and (v, J) = (2,0),(1,5), or (0,9) for NeMu. It is unlikely that just one vibrational level is populated, andcertainly not just one rotational state.Although the present experiments have determined the approximate degree of excitation involved, they put no restriction on the distribution of energy between vibration and rotation. Conventional molecular ions are often formed in excited vibrational150states by electron impact or exothermic charge transfer, although when rotational excitation has been measured [153,215,216] it appears to be high. Furthermore, measurements [79,153,204] and calculations [217] show that ions are excited rotationally as theyare de-excited vibrationally. Perhaps the same process could populate high J states ofHeMu+ and NeMu+ even if these ions are formed with purely vibrational excitation.It appears, then, that the muonated rare gases could well be present with justabout any partitioning between vibrational and rotational energy, and perhaps a widerange. For vibrational levels v > 0 the high-J states are longer lived for radiative decay [75]. It should be noted as well that HeMu and NeMu have rotational energyspacings 1000 cm1 [75], more typical of vibrational spacings than rotational.The reactivity of ArMu+ and N2M11+ follows an entirely different pattern. In argonmoderator, depolarization was seen only for the neutrals nitric oxide and triethylamine,for which charge transfer is exothermic from the ground state of ArMu+. There wasno reaction visible even for tetramethyl silane whose reaction is barely exothermic (table 4.2). This indicates that ArMu is in its ground state, achieved, undoubtedly, byrapid collisional quenching by the Ar bath, and it may be in a cluster with additionalAr (5.2). The story is similar for N2Mu, with only NO giving depolarization. Theseresults agree with the usual finding that N2 and Ar de-excite molecular ions much betterthan do He or Ne [16,79,153,154,156,157,206—208].6.2 The Reactivity of Krypton with NeMuAs reported in chapter 4 and shown in figure 4.3, krypton reacts with NeMu+ even thoughMu formation from ground state NeMu+ and Kr is endothermic by 2.25 eV, and formation from even a bare is endothermic [i.e., IP(Kr) > IP(Mu)] by 0.47 eV. How is thispossible?An artifact due to impure Kr has been considered and rejected (5.3) based on repetitions of the measurement and the absence of any reaction between Kr and HeMu+.151Parallel reactions with any impurity should still give kexp k, just as for the deliberatemeasurements of ternary mixtures (5.4), not the observed kexp << k. Note that Muformation with HeMu+ is less endothermic than the NeMu+ reaction yet there was nocharge transfer seen in He. To add to the puzzle, CO gave no relaxation, although it hasthe same ionization potential and reaction endothermicity as Kr.While it is odd that ke is not zero, it is equally odd that k is so low. The muon-transfer reaction is exothermic, probably by 2.3 eV, so it was expected to proceed ator near the capture rate. Instead, k is just a little greater than ke ( = 0.33vs. ke = 0.23 x 10_b cm3 molec’ s1 in table 4.4), and the total rate constant is just1/16 of kL.There are a number of possibilities for increasing the energy available for Mu formation. Both HeMu+ and NeMu+ have one long-lived quasibound state: the HeMu+v = 0, J = 8 state at 0.029 eV above the dissociation limit with a predissociation lifetimeof 3.5 x i0 s, and the NeMu v = 0, J = 11 state at 0.060 eV having a lifetime of4.2 x 10_6 s [75, see table 1.2]. The former is shorter-lived than a j, but the latter isslightly longer-lived than the muon itself at 2.2 ,us, and so could contribute to the observed reaction. Even from the (juasibound state, however, the charge-transfer reactionof (NeMu+)* with krypton is still 0.40 eV endothermic.This endothermicity may be reduced further if bound NeKr+ was formed by chargeexchange, contributing its binding energy of 0.057 eV [144]. Such “switching reactions”(NeMuj* (J=11) + Kr —* Mu + NeKr — 0.34 eV (6.2)were considered in section 4.2 but, as in this case, the energy difference is not great enoughto have much effect: exp(—0.34 eV/kT) = 10_6 whereas the reaction occurs at 0.06 ofthe collision rate. There are much more strongly bound rare gas dimer ions though; Kris bound by 1.15 eV [144], which is more than enough to allow the reaction(NeMuj* + 2 Kr —* Mu + Ne + Krt (6.3)152to proceed; in fact the minimum excitation of NeMu+ needed is only 1.10 eV—less thanthat for charge exchange with N20! This termolecular reaction could also be compatiblewith the non-reactivity of CO — not on the basis of energetics, but by claiming a slow(CO) formation rate. Other observations are not explained though: the reaction rateis clearly first-order in krypton concentration (see the straight line in figure 4.3); theHe-equivalent of reaction (6.3) is even less endothermic, needing less excitation, but wasnot observed; and there is no explanation of why the muon-transfer reaction would beso slow. The simple-model determination of k,4 listed in table 4.4 is quite uncertain, andit would need reinterpretation if the reaction is termolecular, but it would still need tobe unusually low to achieve such a low kexp. This is made even clearer by considering atermolecular capture and break-UI) mechanism explicitly(NeMuj* + Kr C (Ne Mu I<r )* Kr Mu + Kr + Ne (6.4)k1) k[Kr}k+k[Ne]Ne + KrMuIn this mechanism, as opposed to any considered so far, two Kr atoms react sequentially,and both the initial capture and the subsequent Mu formation should have comparablerates (k k). However, muon transfer (k) should be much faster than this. The kdissociation channel is endothermic (for a ground-state complex) by just 10 kJ/mol,while the k channel is endotherinic 360 kJ/rnol, which is the minimum excitationenergy of (NeMuKrj* to account for the observed depolarization. A simple RRK [218]estimate of k is then(360_ 10)8_1 (6.5)where s is the number of vibrational modes in the complex (or, more typically, about halfthat number), and v can be approximated by a vibrational frequency; in this case, kV 1012 s1. On the other hand, k[Kr] kL[Krl 1O s, so essentially all the reactingions would react by muon transfer, even though Mu formation is energetically feasible.153Another feature of the reaction scheme (6.4), which it shares with the previously-considered capture mechanism (4.19), is cyclic capture and break-up (with the unimolecular dissociation rate constant kb). Rapid dissociation of such a highly energized complexto re-form the original reactants is to be expected, and can serve to reduce kexp below k;in this case kc/kexp = (kb + > = 16. A high kb is to be expected from the lackof available vibrational states in the Ne Mu Kr+ complex. No real calculations have beendone for this (or any of the other) complexes, but this one is only triatomic, and it haslighter constituents (thus, wider rovibrational spacings) than the corresponding triatomicxenon complex. Only He Mu Kr+ is likely to have fewer available states, in accord withthe absence of depolarization there. The problem here is that the excited (NeMuj* ionwould likely not be restored after a cycle of capture and breakup. Instead, quenchedNeMu+ should result, which could not subsequently form Mu, but only KrMu+.In summary, this model has been considered because there is no other apparent wayfor charge transfer forming Mu to occur in the NeMu+ + Kr reaction. It does, however,have several shortcomings:• The complex would likely not last long enough to encounter a second Kr; its breakupwould be rapid, especially through the muon-transfer channel (k). Thus, no chargetransfer should have been seen. Instead, the observed charge-transfer rate was onlymarginally lower than for muon transfer.• No charge exchange reaction was seen for the similar systems HeMu+ + Kr andNeMu + CO.• The mechanism gives a reaction rate that is second-order with respect to [Kr], andthird-order overall, but the observed kinetics were clearly first-order with [Kr].Perhaps the complex is much more long-lived than expected. Perhaps the two Kr atomsare not independent, but are bound as Kr2 — another extremely unlikely circumstanceat the temperatures and pressures employed. Depolarization of KrMu+ due to spin—154rotational interactions could also be considered, thus circumventing the requirement forforming Mu. This effect is expected to be minimal [219], but studies in this directionwould be useful. At the moment, there is no clear explanation for the observable reactionbetween NeMu+ and Kr.6.3 Analysis of Quenching by the ModeratorModerator quenching rates are listed in tables 4.1 and 4.3 but these show a lot of scatterinfluenced by variations in moderator purity. More consistent measurements of kq, madeby varying the moderator pressure with the same reagent gas, were reported in section 4.8.The strongest effect of quenching was on the relative amplitudes of the signals, especiallyfor CH3F, shown in figure 4.7d. The relaxation rates varied less (table 4.6) and, strangely,the total relaxation rate for xenon decreased with increasing pressure.Although variations in the apparent kq, have been attributed herein to impurity(most likely water vapor), there are indications that quenching still makes a contribution.First, quenching of the energized complex could affect the amplitudes more than therates, while a parallel proton (muon) transfer reaction with a dilute impurity is much lesslikely to. Secondly, there are the cases where quenching should have no effect, and theamplitudes did agree with the relaxations.Several of the neutral gases studied are able to form Mu even when the ion is inits ground state, yet excitation might still increase the rate of charge transfer in thosecases as muon transfer is the more exothermic reaction. Nitric oxide and oxygen formparamagnetic ions [152,209] after muon transfer, which should themselves be depolarized, so quenching should have no effect for them. Comparing the values of ‘kq’ derivedfrom the relaxation rates (table 4.1) and the amplitudes (table 4.3) shows relatively lowvalues for these two cases and good agreement between the methods, confirming thatquenching is unimportant for NO and 02, and also suggesting an impurity concentration: {H20] 0.4 x 10_lU cm3molec’ s. This level should be reproducible for exper155iments performed with cold-trapping, or at least for those performed contiguously withthe 02 and NO runs, but kq is often much higher, indicating that quenching is indeedimportant.Some measurements of quenching were made with argon as a collider, but thesediffered from the pressure dependences in that small quantities of Ar (0—2 torr) wereadded to NO/Ne and N2O/Ne mixtures; the NO and N2O served as monitor gases for theNeMu+ excitation. The results of these measurements are shown in figures 6.1 and 6.2.The simple-model prediction is for the relaxation rate to increase linearly with [Ar], andfor A/Af to do the same since k’ = 0:= kjXJ + k[Ar] + k[Ne] (6.6)and- k[Ar] + k[Ar][X] + kD[X] + k[Ne] (67)Af— ke[X1 ke[X]Fits to these equations were used to give the results in table 6.1, using the values of kefrom table 4.4. These fits show again that quenching affects the relaxation rates muchless than the amplitudes, just as happened for the pressure dependences, indicative ofstabilization of the complex. There is also a much greater quenching effect for N2O thanfor NO, with kq + k[X] a factor of 60 larger!N2O has a much higher IP than NO (12.89 vs. 9.26 eV) and will undergo chargetransfer only if the NeMu+ is excited. NO will undergo charge transfer even with ground-state NeMu+; furthermore, any NOMu+ formed by muon transfer will be depolarizedas if it were Mu, so it is to be expected that quenching would have little effect on NOreactivity, and be more important for N2O. The fact that this expectation is borne out(table 6.1) indicates that the argon reaction in N2O/Ne really is collisional quenchingof NeMu+ rather than formation of ArMu+, either initially or through muon transfer.The rate constant determined from the NO relaxation rates is within errors of kq + k[X]I5.04.03.02.01.00.01560 100 200 300 400 500 600 700 80014 —3[Ar] (10 atom cm )Figure 6.1 The effect of argon on the total reaction rate of NeMu+ with N20 (.) andNO () monitor gases. The effect is small in both cases although the N20 results arevery scattered.7.06.05.04.03.02.01.00.00 100 200 300 400 500 600 700 80014 —3[Ar] (10 atom cm )Figure 6.2 The effect of argon quenching on the amplitudes for N20 (.) and NO (o)showing how the endothermic N20 reaction is affected much more by quenching than theexothermic NO reaction. The curves are explained in the text.monitorN20 (U)NO (o)157Table 6.1 Results from Measurements of Argon Quenching of (NeMuj*from )f. from A/AfX [x keb kexp k + k[X] kN20 20.1 8.57 ± 0.68 0.028 + 0.124 1.78 ± 0.27 OC3.1 + 1.1 0.32 + 0.27NO 7.33 6.45 ± 0.80 0.043 + 0.015 0.0302 ± 0.0085 0.00 ± 0.06a Concentrations of N2O and NO were held constant while the [Ar] was varied; concentrations given in 1014 molec cnf3.b Values for ke taken from table 4.4, this thesis. All the rate constants have units of10_b cm3molec’Although ke should be zero for Ar, it gave a higher value in one fit. The uncertaintiesof the points do not support the addition of this parameter; it should be taken as zero.determined from the amplitudes, but the reaction is not really quenching in the NO case.Instead, it is likely to be the muon-transfer reaction forming ArMu+. Of course, thepresence of NO does not stop the quenching process, but merely masks it.The kq + k[N2O] determined by the amplitudes for N2O is 1.78 ± 0.27 x 10’° cm3molec’ s (the solid line in figure 6.2), which, for k = kL = 8.18 x 10_b cm3molec’ s,says that argon quenches NeMu+ with an efficiency of 0.22 —one in five collisions causesde-excitation. This is 11 times higher than the efficiency with which Ar quenches (ArHj*[149, but questioned in 198], it is 150 times tile efficiency for (02j* [153], and verymuch higher than for (NO)* [154], but it is less than the quenching efficiency of Ar on(HClj* [79]. The quenching rate for Ar seems surprisingly high, given the sparse rovibrational states of NeMu. Tichy et al. had a similar surprise in their study of (HC1j*quenching [79].The curved dotted line shown in figure 6.2 is a fit that allowed for some Mu forma158tion (or at least some depolarization) by Ar. Although the fit is ‘better,’ it uses threeparameters for only four points and charge transfer with Ar is simply not possible. Theperfectly reasonable linear fit is chosen instead.Comparing the kq+ks[XJ values determined by the amplitudes for CH3F in table 4.6with the Langevin collision rate shows quenching efficiencies of 0.0004 for He + (HeMuj*,and 0.000 14 for Ne + (NeMuj*. Both are a factor of - 1000 lower than the Ar quenching efficiency, and both are in accord with the usual low efficiencies for He or Ne quenching [16,79,153,154,156,157,206—208]. For the cases of He and Ne quenching, the moderatoris also a constituent of the molecular ion, and the quenching mechanism may be morethan collisional de-excitation, with some ligand switching(NeMuj* + Ne’ —* Ne’Mu + Ne (6.8)occurring as well. Such an exchange should be more effective than a simple collision for removing vibrational excitation. Exchange is not absolutely necessary for this effectiveness,however. If there is an intimate collision to form a transient Ne2Mu+ complex whereinvibrational energy is randomized, it is immaterial which Ne eventually leaves. Since theobserved quenching efficiencies were so low, this type of switching appears unimportant.As stated, the relaxation rates are not much affected by quenching, whether byadded Ar or by the Ne bath gas, while the amplitudes are (tables 4.66.1). This difference was interpreted as being due to quenching of the association complex, with ratek[Ar][NeMuN2Oj,or the apparent overall rate k[Ar][NeMuj. The difficulty with thisinterpretation is similar to that for the termolecular Kr reaction model in section 6.2: thecomplex should have too short a lifetime for it to collide with Ar at the concentrationsutilized. On the other hand, the lifetime of NeMuN2Omay be much longer than forNeMuKr+. Note that muon transfer to Ar, which should also be expected to occur, wouldhave the same effect on the relaxation rates as on the amplitudes, just as was observedfor the NH3 monitor ion measurements of the C2H6 and H2O reactions (table 5.4).159An alternative explanation for the pronounced effect of quenching on the amplitudesrelative to the relaxations is that quenching of (NeMuj* may not produce ground-stateNeMu+; instead, a lower excited state should be populated for which charge transfer(depolarization) is still possible, i.e., a state still above the threshold for charge exchange.This lower state would presumably have a much higher k,j/ke branching ratio, but stillbe capture-limited. Other experiments [79,201,202,220] have seen endothermic reactions‘turn on’ when excitation reaches threshold (which is how the simple model treats quenching) but still increase a lot as the excitation is increased further [156,221]. Furthermore,when endo- and exothermic reactions compete, as is the case here, the exothermic reaction rate may also decrease with excitation level [220]. Such behavior would causekjke to increase with decreasing excitation, to give the observed trends in the amplitudes while the continued presence of depolarization would keep the total relaxation ratenearly constant. Two inconsistencies with this description, though, are that there maynot be enough states available in HeMu+ or NeMu+, and different reactants (N20, CH3F)with different thresholds behave qualitatively the same. It is too unlikely to have deexcitation to a state just above threshold in each case, especially when there are so fewstates available.This “weak quenching” picture makes more sense for stabilization of the loosely associated capture complex, which would affect the branching ratio of the reactions from thecomplex in the way just described. There could still be some degree of direct quenchingof (NeMuj*, along with muon transfer producing ArMu+ to give the (small) increase inrelaxation rate with quenching and the non-zero intercepts of vs. [X].There is wide scope to extend these measurements: by varying the neutral reagent(the monitor, X) to set different reaction thresholds, l)y varying its concentration lookingfor evidence of termolecular quenching Ar + X + NeMu+, by varying the quencher, andby studying quenching of (HeMuj*.1606.4 Neon Moderator Pressure and the Xe + NeMu+ ReactionThe case of xenon is interesting, albeit confusing, with many anomalies not understandable within a simple competition-kinetics model. Noteworthy are the consistently lowexperimental “capture” rate constants reported in tables 4.1 and 4.4, for both He andNe moderators—only half the Langevin predictions. Xe + NeMu+ is such a simple system that the Langevin rate should give the real collision rate. The measured rates alsoexhibited an unusual reverse pressure dependence (table 4.6, figure 4.9), decreasing withincreasing moderator pressure. Less consistently, Xe measurements have given curvedkinetic plots, which delayed understanding the processes involved, if indeed they areunderstood yet.Is the unusual behavior of xenon mere perversity, or is it made understandable bya more sophisticated kinetic model? What features must such a kinetic scheme haveto reproduce the observations? Answering these questions consumed a disproportionateamount of time and effort in comparison with elucidating the simple capture kineticsexhibited by other reactants. Like the krypton conundrum, there is no single satisfactoryanswer, but an exploration of the possibilities is useful. One option would be to dropthe notion of ion—molecule capture entirely, but that would be rash. If the measuredrates were much faster than the Langevin capture rate, it might be necessary to invokelong range interactions that supersede capture, but the actual rates are lower than thepredicted capture rates so it is reasonable to say that the initial capture still operates,but it is not the limiting step because of rapid breakup.As a start to understanding the pressure dependence of the ‘fast’ relaxation )j forXe + NeMu, with reference to table 4.6 note that the simple-model (linear) fits gavenegative values for “kq” that were roughly proportional to Xe concentration. Thus, without defining k9, ) k[Xej — k?[Xe] [Ne], where k need not be the real capture rate.On the surface, none of the models considered in chapter 4 give this behaviour, but on161closer examination the general mechanism of cyclic capture and breakup (4.19) may wellapply if the dissociation of the complex could involve the moderator, with kb replacedby kb[NeJ. The limiting solution (4.31) can then be expressed as— k[Xe](k + k) 6 9— k[Xe] + kb[Ne] + k + kwhich, for large values of k + k is approximated by— k [X — (k[Xe])2 — k[Xe] kb[Ne] 6 10—ek+k k+k[by expanding around 1/(k + k) = 0], which closely matches the desired behaviour.Based on this promising approximation, the measured rates were fitted using thegeneral expression for )_, eq. (4.29), giving the curves displayed in figure 6.3. The agreement with the data is remarkable, including the points at [Xe] = 44.5 x 1014 moleccm3,[Xe] = 50.5 (.), 44.5 (0), 14.4 (.)3.5 I I0 500 1000 1500 2000 2500Ne Pressure (torr)Figure 6.3 Simultaneous fits of equation (4.29) to the neon pressure dependenceof the fast relaxation rate for three concentrations of xenon: 50.5 (.), 14.4 (.), and44.5 (o) x 1014 molec cm3. Tile two variable parameters were determined to be kb =2.78 + 0.34 x i0’4 ciii3 atom’ 1 and k + k = 2.86 + 0.15 [ts’, with k fixed at11.23 x 10_lU cm3molec s, the Langevin value. Releasing k gave an almost identical fit.162Table 6.2 Results of Fits to the Xe + NeMu Pressure DependencesFit what, with what kbb k + kAll points, all variables 13.4 + 1.4 4.5 ± 1.2 3.06 + 0.2044.5 points omitted 13.5 + 1.5 4.3 ± 1.3 2.93 + 0.22All points, k fixed 11.23 2.78 + 0.34 2.86 ± 0.15No 44.5 points, lc fixed 11.23 2.60 + 0.34 2.74 ± 0.17a 10_b cm3molec’ —i• b 10_14 cm3 atom’ cwhich were at first thought to be amiss. If the fit is performed omitting these points, theresults are almost the same, indicating that both the data and the fits are reasonable.Fits were done with k both as a free parameter and fixed at its Langevin value. Withthe capture rate variable, it became slightly higher than the Langevin value, althoughthe difference is barely significant. The results of all these fits are shown in table 6.2.One point of passing interest is that the curves in figure 6.3 have very similar slopes, eventhough an expectation of varying siopes led to the consideration of this model.Why should there be a discernable back reaction for xenon, but apparently not forother neutrals? Perhaps it is the lack of vibrational modes among which to distributethe excess energy of (Xe Ne Mu+)*, making it susceptible to rapid breakup. This hasalready been indicated for the Kr case. Or maybe the unimolecular rate constants k andk are unusually low, as indicated by the fits, giving more time for breakup. These twopossibilities are antagonistic in that instability of the complex should promote all forms ofbreakup, including dissociation into products. A large barrier to Mu+ transfer within thecomplex would be necessary for such a low k. In addition, what role could the moderatorplay in the back reaction? Thermal collisions should stabilize the complex rather thanbreak it apart. The moderator-mediated breakup fits the pressure dependent reactionrates well, but seems physically untenable, and leaves many unanswered questions.163This mechanism partially accounts for curved vs. [Xe] plots (fig. 6.6) because ofthe ‘fall-off’ regime where )_ ), with the rate leveling off at k + k = 3 zs1 at highxenon concentration. Yet this does not agree with the straight lines that were usually seenfor Xe (and for other reactants) including maximum relaxation rates well above 3 ts’.Despite its partial success in describing the reaction rates, the cyclic capture mechanismdoes not agree with other aspects of the Xe results. The amplitudes of the two components would not vary with Xe concentration under such a mechanism, in contrast to themeasurements listed in tables 4.3 and 4.6 (see also figure 4.7). And surely, there shouldbe quenching of the (NeMu+)* through a cycle of capture and breakup. Additionally, theobserved signals did not show the two-fast, one-slow relaxations predicted by this, andthe other, explicit capture models. While this last difficulty may really be no problem atall, there are too many contradictions to take the good fits at face value.6.5 Modeling the Anomalous Xenon ResultsBesides having varying non-linearly, one set of results Xe in Ne at 177 K — showedthe ratio A/Af non-linearly decreasing with Xe concentration (illustrated below in figure 6.6) whereas it increased linearly within most sets of Xe (and other) data in accordwith the simple model prediction, eq. (4.13). Such a unique anomaly is easy to dismiss,especially since a non-relaxing wall signal, if left unaccounted for, could cause the sameresult; but other data taken at the same time show no such behavior, indicating that thexenon reagent might be responsible. The following explanation has some major difficulties, and it should not be taken too seriously, but it is presented nonetheless as it haswider implications for the application of the general capture mechanism (4.19) to the tSRresults.As mentioned in the previous section, ion—neutral capture to form a long-lived complex, as in mechanism (4.19) should match the observation of the vs. [Xe] line curvingdown at high xenon concentration: the rate of the second (unimolecular) step, which is164independent of reactant concentration, places an upper limit on the overall reaction rateso the line must curve as this limit is approached. In general, downward curving (concave)rate curves are indicative of sequential reactions of different order while upward curving(convex) curves come from parallel reactions. The strange behavior of the amplitudesin the same series of runs may indicate that the depolarizing (charge-transfer) reactionchannel loses effectiveness relative to other channels as Xe is added. To achieve this behavior, xenon must be involved in the secondary reactions, either interfering with chargetransfer, or contributing to other channels. One candidate for such a process is collisionalde-excitation of the capture complex by the reagent: Xe is a much better quencher thanHe or Ne [157,190]. Such a process, with rate constant k [eq. (4.19)] can be regardedboth as a competing reaction channel and as a process interfering with charge exchange.The expectation expressed in section 4.5 was that k could be ignored because it wouldbe much lower than the competing rates. The fits in the previous section gave very lowbreakup rates, so may be considered anew.Ignoring the pressure dependence for the moment, there is one other requirement fora successful description of the Xe reaction: the deviation from a simple two-componentrelaxation envelope must be small. This requirement is demanded by scrutiny of theactual histograms which revealed no extra relaxation components. As mentioned in section 4.6, such components are to be expected of a two-step mechanism when the rates ofthe two steps are different but comparable.165A mechanism intended to meet these requirements is:Mu + Xe+ Nekk(NeMu+)* C (NeMuX&j* XeMu + Ne (6.11)XekqNe kjXe /NeMu+ NeMuXe+.The channel for collisional stabilization of the capture complex by Xe, with a rate ofk[Xe], produces NeMuXe+, which no longer has sufficient energy to undergo charge transfer, so it is limited to forming diamagnetic XeMu. This mechanism clearly meets therequirements of being two-step with a second Xe atom participating in the secondaryreactions, although it is not obvious that it could produce spectra with apparently onlyone relaxing component. The time dependence of the diamagnetic signal (or of the concentration of all diamagnetic species) is1_ni 7 / —)2t 1t—3+e e 612[D]0—A1.)2)‘1 — 2 “ ‘‘2where= kk[Xe]A2 =k+k+k[XejA3 = k{Xe} + kq[Ne]which is a slight simplification of the similar mechanism (4.30), but such a dependencewas originally rejected because the form of the observed relaxation didn’t support it. Thetime has come for a second look.1660.300.200.10—0.10—0.20—0.300.04__0.02I iE—0.06—0.080.0 1.0 2.0 3.0 4.0 5.0 6.0Time (p.s)Figure 6.4 The simple model fitted to a representative synthetic data run based on theXe model showing the asymmetry signal on top and the difference between the points andthe fit below. Although the points were generated with three components to the relaxation and fitted with only two, there is hardly any residual signal in the lower plot (notethe expanded scale there). This run corresponds to the [X] = 40 x 1014 moleccm3pointof figure 6.5167To investigate whether a three-component relaxation could appear to have only twocomponents in the present experiments, and also to assess the relevance of the specificXe capture/quenching model, several runs were simulated with ‘decay’ asymmetries givenby equation (6.12) using a wide variety of values for the relevant rate constants but withthe capture rate always set to 11 x 10_b cm3 molec s1, the Langevin rate. Randomscatter was given to the points using the counting statistics appropriate for a better-than-typical run (4 million events). The runs were then analysed according to the simple modelwith only two components to the relaxation. For most combinations of parameters the fitswere surprisingly good, with the residual signals not visible against the random scatterof the points. One representative run is illustrated in figure 6.4, with the asymmetry ploton top and the difference between the data and the fit shown as difference in asymmetrybelow. The fit gives a relaxation rate of = 1.71 jis which is not closely related toany of the input parameters. Indeed this is the general situation—good fits which donot give back the input parameters. Good fits were expected for limiting cases with onestep much faster than the other, but this result was a surprise. Moreover, it was verydifficult to find combinations of parameters that did not give straight or near-straightvs. concentration plots, such as figure 6.5.What, then, of the curved plots of both and A5/Af (figure 6.6) for the Xe reaction?Parameters were found that do mimic this behavior: k, k, and kq[M] = 2.7, 0.6, and0.0 ts1 respectively, with lc = 11 and k = 0.9 x 10_b cm3molec’s1, giving the resultsshown in figure 6.7. The remarkable similarity of figures 6.6 and 6.7 demonstrates theviability of both the mechanism and the specific parameters used, but it does not amountto a measurement of those parameters. Nevertheless, these values can still serve as aguide to the relative importance of each channel. In particular, note that k is only 1/12the value of k, yet it has a great effect on the amplitudes, causing A/A to decreaseinstead of increasing with reciprocal concentration, and to curve in just the way that theXe results do.168The other notable parameter is kq, which has a value of zero, effectively nullifyingthat channel and simplifying the mechanism toMu+Xe + Nek(NeMuj* k + *(NeMuXe ) XeMu + NeXekXeNeMuXe/(6.13)leaving no moderator effect, in disagreement with the data. This is a serious blow, especially after the cyclic capture model fit the pressure dependences so well.U)‘IFigure 6.5 The near-linear dependence of on idealized reactant concentration for aseries of synthetic runs showing an apparent k = 3.7 x 100 cm3molec’ s although thevalue used to generate the data was k = 11.0 x 10b0 cm3rnolec’ s1. Other parametersI —1 I—I . —10 3 —1 —1 —1were ke = 1.5 ts , = 0.2 jts , = 3 x 10 cm molec s , and kq[M] = 0.1 its4.03.02.01.00.00 20[X]40(101460 80—3molec cm )1001693.5 I I1.51.00.50.0 I I I0 20 40 60 80 100[Xe] (1014 molec cm3)0.50 I0.400.300.20:: I I0.00 0.02 0.04 0.06 0.08 0.10 0.12—1 —14 3 —1[Xe] (10 cm moec )Figure 6.6 Experimental results for Xe + NeMu at 177 K showing the non-lineardependence of on [Xe] (top) and the very unusual decrease in A/Af with [Xe]’ (bottom).170I I Iç2.o1.51.0U0.50.0 I I0 20 40 60 80 10014 —3[X] (10 molec cm )0.50 I I I I0.40+0.20+0.10+0.00 I I I0.00 0.02 0.04 0.06 0.08 0.10 0.12—1 —14 3 —1[X] (10 cm molec )Figure 6.7 Results synthesized to mimic the Xe data shown in the previous figure.Each reactant ‘concentration’ [X] corresponds to a histogram generated using the parameters given in the text, and analyzed according to the simple model.171Since only one set of data in fact showed the unexpected increase in AS/Af withXe concentration, invoking special mechanisms to explain these results is probably notwarranted. The cause is more likely to be an isolated spurious artifact of muons stoppingin the target walls; the diamagnetic SR signals of a molecular ion and of a muon in aluminum are virtually indistinguishable, and it is very difficult to ensure that all muons stopin the gas. Measured values of A were always corrected for the wall signal amplitudes,and the corrected amplitudes usually behaved as predicted, but if the wall correction usedwas too small, the resulting inflated values for A could give just the dependence shownin figure 6.6 (top). The results seen at 177 K were not observed in any other Xe data,suggesting that they are such an artifact, even though ‘normal’ results were obtained forother reagents just before the Xe runs were taken. It is likely that for the one anomalousseries of Xe runs, some shift in the beam tune or apparatus position caused an increasedwall signal that went unnoticed, so it is best to just ignore the unusual amplitudes.It is possible for a wall signal to interfere even more insidiously when it has a slightlydifferent frequency, phase, and/or relaxation rate from the molecular ion signal. The obvious solution is to include all the wall signal parameters in the analysis of each histogram,but this does not work. As shown by the synthetic data presented in this section and byexperience with actual runs, signals with extra components are fitted well by a simplerfunction, while the introduction of extra parameters leaves the function over-determinedand insensitive to the chemical signal. The magnitude of this problem depends on thenatural amplitude of the relaxing component: when the amplitude is small, the wall problem is severe. The amplitudes depend on reagent concentration, and when the influenceof the wall signal varies with the concentration, curved kinetic plots may result.With these considerations, it is reasonable to abandon the special-purpose Xe capture/quenching mechanism (6.11), and attribute the anomalies observed at 177 K to wallsignals. But the modeling of those (unreliable) results has shown that an extraordinarily long-lived complex could be accommodated within the present data with only a172two-component relaxation observable. The relaxation function of the xenon model, equation (6.12), is really no different from that of the generalized capture model, given inequation (4.30); in particular, both can be fitted well by the simpler equations (4.26),(4.16), or (4.32) to give values for that depend linearly on concentration. The implication is that straight lines might not always give the capture rate; subsequent reactionsmay affect the overall rate with no outward indication. Such cases cannot be identifled by their multi-component relaxations. In addition, when deviations from the simplemechanism are evident, it is not practical to fit the data assuming a more complex mechanism because several different models may fit equally well. This was mentioned earlier,but it bears repeating: the capture mechanism places an upper bound on the overallreaction rate, but not all “kexp” rate constants reported in this thesis are capture rateconstants—some of the reactions are not capture limited. The difference between kexpand the calculated k (kL, kAADO; see tables 5.1&5.3) indicates the extent of the departurefrom simple capture kinetics.In figure 6.7, note that there is an apparent intercept, )f(O) > 0, even though a valueof kq = 0 was used to generate the data. This casts doubt on the general interpretationof such intercepts as giving kq[M]. Such an interpretation already had problems though,as the values were not the same for different reagents X, probably because of impuritiesin the moderator gas.6.6 Weak Quenching of the Capture ComplexThe results of modeling have shown that the Xe and Kr data are insufficient to fullydetermine the reaction mechanism involved; such attempts lead to unrealistic models—ones with very long-lived complexes and moderator-assisted breakup. Measurements ofquenching by Ar and Ne showed that stabilization of the complex is more effective thanquenching of the initial excited ion. An acceptable model of this stabilization must bemore intuitively satisfying.173Returning to the reverse pressure dependence of the Xe reaction rate, it certainlyseems reasonable that the increased quenching at higher pressures would decrease the rateof the endothermic Xe reaction, which relies on reactant excitation. Such a mechanismwould necessarily involve ‘weak quenching’ whereby each collision with the moderatorgas decreases the excitation energy slightly. In particular, each collision with Ne mayreduce the excitation of (XeMuNej* slightly, reducing the rate of uriimolecular Mu formation, k(E):Mu-j-X+Mke(E)/(M(MMu+)* + X k(E) (6.14)(MMuX+)*k’(E)\XMu+M.The weak quenching is represented by the vertical dots, indicating that the excitationenergy E in the complex declines at a rate of k(E).This is a much more realistic model of quenching than the strong quenching mechanism assumed so far; in a single collision, a small moderator atom like He and Ne cannotcarry away enough energy to fully stabilize an excited ion. The (He) pressure-dependentassociation rate of CH + HCN indicates an average energy loss of only 0.015 eV per Hecollision [37,222], and quenching by Ne should not be much stronger [37,153,156,157].For reactions of the muonated ions, there is good reason to believe that such quenching operates on the capture complex rather than on the muonated rare gas ion: theexpected energy loss of 0.015 eV is less than the smallest rotational spacing of NeMu+!(The spacings of HeMu+ are even larger [191].) The low density of rovibrational statesin the muonated ions makes weak quenching nigh impossible.’ On the other hand, polyatomic capture complexes have smaller vibrational/rotational energy spacings, particuAlthough it is certainly more viable for quenching of rotational excitation than174larly for the overall rotations and any vibrations not involving Mu. The measurements ofquenching by Ar in the N20 + NeMu reaction, and by Ne for CH3F+ NeMu, indicatedalso that the complex itself was quenched because the amplitudes were affected muchmore than the relaxation rates. Note that, before stabilization, the association complexhas the same total energy as the reactants, which amounts to a greater excitation energy because it has a lower ground state. After quenching below the threshold for Muformation, a complex will dissociate by expelling Ne(He) to form XMuhOnce the excess energy in the complex falls below the threshold for ejection of Mu,charge transfer is impossible, so this threshold could give behavior resembling a strongcollision model (with some efficiency factor) as was assumed for the previous kineticsmodels, especially eq. (4.12). However, as the energy declines towards threshold, themicroscopic rate constant for Mu formation k(E) will decline [130,223], in accord withthe microcanonical TST/RRKM expressionk’ E— W(E— E0) — fE_EQ p(E) dE6 15e( )- hp(E)- hp(E) Lwhere E0 is the minimum excitation energy needed for Mu formation, and p and p arethe densities of states in the (already excited) complex and the transition state for Muformation from the complex, respectively. Stabilization competes with dissociation intoreactants, dissociation into diamagnetic products (muon transfer, at k) and de-excitationby (weak) moderator collisions.The difficulty is that the calculation of the total rate constant (the expected kexp)must follow a statistical model [222,224—226] rather than simple competition kinetics;it must integrate all rate constants over the time-varying distribution of excitation energies E(t). An exact description of the intermediate complex, including vibrationalvibrational; “weak vibrational quenclimg” is a contradiction in terms for HeMu+and NeMu+.175frequencies, is needed before the various microscopic rates [k(E)’sl can be calculated, andthere must be some measure of the energy distribution of the reactants. More work isneeded on both fronts.In the simple kinetic models used to evaluate the data, quenching by X was includedwith the muon-transfer reaction channel as the two were experimentally indistinguishablefor a strong collisional quenching model. For weak quenching, however, collisional stabilization by the neutral reactant would need to be accounted for separately. Since partialde-excitation should decrease the reaction rate, quenching by Xe itself might provide yetanother explanation for the curved A vs. [Xe] sometimes obtained.All the mechanisms considered to explain the unexpected results from xenon (andkrypton) have explicitly involved a capture complex existing for some time, but resultsfor the many other systems investigated give no explicit indication of a capture mechanism, beyond having overall rates that agree with the theoretical capture rates. Capturetheories place no special reliance on long-lived complexes, only on the overwhelming influence of the long-range attractive potential, so the many experimental rate constantsprobably indicate a short-lived capture complex. It is hard to understand how a simplecomplex like NeMuXe+ could be long-lived when a much larger conglomeration such asNeMuCH3Ot is short-lived; surely the many degrees of freedom in the latter could keepit together longer. Could there be a barrier to internal rearrangement that dramaticallystabilizes the smaller species?“Long-lived” in the context of these experiments is of order 1 xis, which is still veryshort compared to the time-scale in a typical study of ion—molecule reactions (1—100 ms),so an enhanced lifetime could have gone unnoticed in other experiments; but 1 its is stillvery long in the time frame of elementary reactions, and is i05 times longer than theexpected lifetime of the transient complex. Yet there is evidence that the intermediatecomplexes of xenon, krypton, and probably the fluoro-alkanes, are long-lived relative tothe 1 its time frame of these experiments, and relative to the fleeting existence of the176intermediates in the other reactions. It is noteworthy that the majority of reactions studied showed no evidence for intermediate complex formation except for reacting at theirpredicted capture rates. For whatever time the complex exists, collisional stabilizationappears to operate much more efficiently on the short-lived association than on the original ions, which are amazingly resistant to rovibrational de-excitation, a result, no doubt,of the very low density of their vibrational and rotational states.Chapter 7SUMMARY AND CONCLUDING REMARKSThe principal goal of these experiments was to use the technique of muon spin rotationto study the ion—molecule reactions of the muonium isotopomers of the protonated inertgases: HeMu+, NeMu+, and, to some extent, ArMu+ and N2Mu+, and in so doing, provide an extensive new body of data on the reactivity of these, the simplest closed shell(point charge) molecular ions, which could also be applied to their protonated cousins.This goal has been met, with the measurement of muon-transfer (like proton-transfer)reactions and, particularly, charge-transfer reactions for a wide variety of reactants ofdiffering polarizabilities and dipole moments.A related goal, to compare with corresponding studies of the protonated rare gases,has been frustrated somewhat by the lack of data on molecules of common interest. Bystudying the muonated analogs of l)rotonated ions, it was hoped that mass effects wouldbe made evident, especially the influence, if any, of quantum tunnelling in ionic reactions. Also, since iSR facilitates measurements at much higher pressures than possiblewith conventional techniques, the effect of moderator density could be investigated. Yetthe comparisons made with protonated ion studies indicate that neither high pressurenor quantum tunnelling are particularly important for the proton- (muon-) and chargetransfer reactions studied. This is, in itself, an important conclusion.1771787.1 Reaction RatesIon—molecule reaction rates were measured for the muonated inert gas molecular ionsHeMu+, NeMu+, ArMu+, and N2Mu+ reacting with a wide variety of polar and nonpolar neutral species (tables 4.1—4.4 & 5.4), at various inert gas pressures in the range400—2400 torr, and at various temperatures from 120 to 450 K, with most experimentsperformed at room temperature. In almost all cases, both charge transfer (which causesdepolarization) and muon transfer (which does not) were observed, manifest as a two-component decay of the SR signal, where the relaxation rate is interpreted as the totalreaction rate, and the ratio of the amplitudes is indicative of the product distribution(the ‘simple model’, §4.4). Since charge transfer is endothermic for ground-state reactants in many cases, the reaction is believed to occur from rovibrationally excited statesof (HeMu+)* and (NeMuj*, with approximately 1 eV of excitation energy.The experimental rate constants are generally in very good agreement with the theoretical (AADO [117] or Langevin [110]) maximum values, demonstrating anew the viabilityof simple capture theories. In comparing the various formulations for ion—dipole capture,it appears that the AADO [117] and parameterized trajectory [118] calculations give thebest upper limits on the reaction rates. Several temperature dependences (120—450 K)were measured which agreed satisfactorily with classical AADO capture theory, showingno great deviations at ‘low’ temperatures characteristic of quantum-mechanical capturetreatments. Reactions of some neutrals were observed to be significantly slower thanthe capture predictions: Xe, Kr, CF4, CH3F, and C2H4F, typically giving only halfthe theoretical maxima, but with Kr reacting at oniy 1/16 of the Langevin rate. Theseexceptions might be due to formation of very long-lived complexes (‘-- 1 s) and/or theback-dissociation of such complexes before charge transfer is accomplished, though neitherinterpretation is straightforward. The majority of cases that agreed closely with capturetheory must similarly react through an intermediate complex, although the complex may179be very transitory and rapidly dissociate into products.Comparing the results of the present experiments with the few corresponding protonated ion measurements shows a high level of agreement for the total reaction rates, bettereven than the correspondence between experiment and theory. Reactivity of the protonated rare gases is dominated by proton transfer, with charge exchange being reported inonly a few cases with HeH+ and NeH+ [191] when these ions are vibrationally excited—analmost identical situation as for the present experiments— and the prevalence of chargetransfer for the molecular ions is attributed to increased excitation rather than toa kinetic isotope effect. Although the reactant ions were rovibrationally excited, whichenhances charge transfer over muon transfer, the total reaction rates were apparently unaffected by the excitation. There is certainly no indication of a significant isotope effecton the total reaction rates. The general level of agreement between the ion—moleculereactivity of the protonated rare gases, at pressures often substantially less than 1 torr,and their muon ion counterparts, above 1 atm, demonstrates that there is no significanteffect of total pressure on these simple reactions, indicating that long-lived intermediatecomplexes are not involved. Transient coml)lexes could still be formed, however, basedon the agreement with capture theory, but they must be short-lived, compared with the1 fts reaction times investigated, and they must form products rather than dissociatinginto reactants. The expected lifetimes are in the range 1O_12 10_b s, although detailed(ab initio and RRKM) calculations were not performed.The reaction of Xe with NeMu+ had anomalies that could indicate a much longerlived intermediate complex. Likewise for Kr + NeMu+, which may actually be second orderin Kr concentration, and third order overall, with formation of Kr to allow otherwiseendothermic charge transfer to occur, although it appeared bimolecular over the [Kr] rangeinvestigated. These exceptions are in contrast to the results for most other neutrals.There was no observable reaction (no charge transfer) with Kr and HeMu+. Otherneutrals which exhibited no charge-transfer reaction were H2 and CO (none was expected180for these), CH4,H20, and CH3N. Muon transfer does occur, at near the capture rate,for H20 and CR4 as measured by a modified monitor ion method. This is interpretedin terms of enhanced muon transfer (perhaps due to muon tunnelling) though there isno definitive explanation; these molecules are not anomalous with respect to other reactions [25,57,147,148,154—156,191—196,198,199] they undergo.While muonated molecular ions were observed for (and in) He, Ne, Ar, and N2 moderators, neither the ions H2Mu+ nor C2H6Mu+ were seen. It is expected that, if formed,these ions immediately react with the respective moderator gas to place the Mu in aneutral molecule, HMu, C2H5Mu, or the stable ion C2H4Mu+. It is more likely that nomuonated ions are formed in these gases, with the diamagnetic ff signal in H2 and C2H6gases attributable to epithermal reactions of neutral Mu.7.2 Ion Formation, Excitation, and QuenchingSince charge transfer was observed in many cases where it is endothermic from theionic ground state, the reacting molecular ions are believed to be rovibrationally excited:(ReMuj* and (NeMu+)*. Rather than acquiring this excitation through energetic collisions, it is believed that the energy is left from the initial formation of the ions byassociation of Mu+ (i.e., a bare tj with He or Ne. The ions are remarkably resistant tocollisional quenching by the bath gas, due both to the very low density of their rovibrational states [191], and to the low quenching efficiencies of He and Ne generally.At the time of reaction, the (HeMuj* and (NeMuj* ions still have 1 eV of excitation, as indicated by their charge-transfer reactions with CF4,N20, and other neutrals(see table 4.2). This corresponds to v = 2 or to a lower vibrational level with some degreeof rotational excitation. Charge transfer was seen with ArMu+ only for triethylamine andnitric oxide, for which the reaction is exothermic from the ground state of ArMu+, indicating that, whatever the initial excitation, it has been effectively removed by the Armoderator gas.181Measurements of de-excitation of HeMu+ and NeMu+ by collisions with the respective moderator or by argon were also l)erfOrmed. The effect on the product distributions(amplitudes) was much greater than on the total reaction rates, which is taken to indicatea weak quenching mechanism whereby a small portion of the excess energy is lost witheach collision. Based on the amplitudes, the quenching efficiency for Ar was found tobe kq/kL = 0.22 ± 0.03, while He and Ne are much less efficient at 0.0004 and 0.00014respectively. This is the same trend found in other studies [79,153,154]. Since the HeMuand NeMu+ ions have such wide rovibrational spacings, they are not good candidates forweak collisional quenching. From this, and from the lack of effect on the total reactionrates, it is argued that quenching is accomplished mainly by third-body collisions on thetransient capture complex (e.g., Ne+XeMuNej, though this assignment of a mechanismis much less certain than the observation of quenching itself.7.3 ProspectsThe 1tSR technique used for this thesis allows measurement of ion—molecule reactions inregimes far removed from those accessible to other techniques. By following one muon ata time, all ion—ion interactions are eliminated, and all other reacting species are unseen.Muon spin rotation is useful for observing fast reactions, particularly reactions of unstablespecies, as all reactions observed must have rates of 0.1—10 set by the mean lifeof the j radioactive decay (2.2 [Is). This can also be a limitation if one wants to studyslow reactions, but the vastly different time range is complementary to other techniques.The high pressures accessible to ,aSR experiments also complements other methods well,allowing measurements from “-j i0 torr (ICR) to 1000 torr ([ISR) and higher.These advantages apply only to the positive rnuoii analogs of protonated ions ofcourse. Instead of observing reactants and products directly, [ISR tracks the magneticenvironment of individual muons. This is very useful for observing spin interactions, butmakes it difficult to study mechanisms with more than one reaction, as the products182usually cannot be detected individually, though diamagnetic and paramagnetic productscan be distinguished. The initial reactants cannot be selected as in a SIFT apparatus,which further limits the ions amenable to study.The greatest contribution of tSR to the field of chemical kinetics, though, is itsdetection of large kinetic isotope effects in many systems [29—31,82]. Such effects on thereactivity of muonated ions were found to be much smaller than those observed for neutralreactions.This thesis has demonstrated the usefulness of jiSR in measuring several ion—moleculereaction rates, the majority of which have not been studied for the corresponding protonated ions. Charge transfer was usually seen, although studies of protonated ions aredominated by proton transfer [24—26], but for the total reaction rates, there was a remarkable lack of isotope effects to be seen in making comparisons with earlier work [25,191,203].Since the substitution of Mu for H has little effect, it is likely that these studies will notbe immediately pursued due to the difficulty and expense of using a high energy particleaccelerator (TRIUMF) to generate muons. Any further measurements will take directionfrom studies using conventional methods, answering questions particularly suited to theILSR technique. It is hoped that this thesis will help spur others to undertake much moreextensive and detailed studies of the reactions of the protonated rare gases, which couldanswer some of the questions raised by this work, and raise new questions that could beanswered, in turn, by iSR studies.References1. A.J. Dempster, Phil. Mag. 31 (1916) 438.2. H.D. Smyth, Phys. Rev. 25 (1925) 452.3. T.R. Hogness and E.G. Lunn, Phys. Rev. 26 (1925) 44.4. V.L. Tal’rose and A.K. Lyubirnova, Dokl. Akad. Nauk SSSR, 86 (1952) 909.5. T.D. Mark and A.W. Castleman, Jr., in Advances in Atomic and Molecular Physicsvol. 20, D. Bates and B. Bederson, eds. (Academic, Orlando, 1984) 65.6. D. Smith and N.G. Adams, J. Chem. Soc. Far. Trans. 285 (1989) 1613.7. G. L. Verschuur, Sky & Telescope, April 1992, 379.8. W.D. Watson, Astrophys. J. 188 (1974) 35.9. A. A. Viggiano, F. Howorka, D. L. Aibritton, F. C. Fehseufeld, N. 0. Adams, andD. Smith, Astrophys. J. 236 (1980) 492.10. E. E. Ferguson, F. C. Fehsenfeld, and D. L. Aibritton, in Gas Phase Ion Chemistryvol. 1, M.T. Bowers, ed. (Academic, New York, 1979) 45.11. D. A. Williams, in Galactic and Extragalactic Infrared Spectroscopy, M. F. Kesslerand J. P. Phillips, eds. (Reidel, New York, 1984), pp. 59—67.12. T. G. Phillips, 0. A. Blake, J. Keene, R. C. Woods, and E. Churchwell, Astrophys. J.294 (1985) L45.13. J.-P. Maillard, P. Drossart, J.K.G. Watson, S.J. Kim, and .J. Caidwell, Astrophys. J.363 (1990) L37; P. Drossart, .J.-P. Maillard, J. Caidwell, S.J. Kim, J.K.G. Watson,W. A. Majewski, J. Tennyson, S. Miller, S. K. Atreya, J. T. Clarke, J. H. Waite, Jr.,and R. Wagener, Nature, 340 (1989) 539.14. S. Miller, R. D. Joseph, and .1. Tennyson, Astrophys. .1. 360 (1990) L55.15. S. Lepp, A. Dalgarno, and A. Sternberg, Astrophys. J. 321 (1987) 383; S. Lepp andA. Dalgarno Astrophys. J. 358 (1990) 262.16. W. Wagner-Redeker, P. R. Kemper, M. T. Bowers, and K. R. Jennings, J. Chem.Phys. 80 (1984) 3606.18318417. I. Dabrowski and 0. Herzberg, Ann. N. Y. Acad. Sci. 38 (1977) 14; I. Dabrowski,0. Herzberg, and R.H. Lipson, Mol. Phys. 63 (1988) 289; I. Dabrowski, G. Herzberg,B.P. Hurley, R.H. Lipson, M. Vervloet, and D.-C. Wang, ibid. 269.18. J. M. Moorhead, R. P. Lowe, J.-P. Maillard, W. H. Wehlau, and F. P. Bernath, Astrophys. J. 326 (1988) 899.19. K.-P. Cheng and F. C. Bruhweiler, Astrophys. J. 364 (1990) 573.20. W. Roberge and A. Dalgarno, Astrophys. J. 255 (1982) 489.21. B. Zygelman and A. Dalgarno, Astrophys. J. 365 (1990) 239; B. Zygelman, A.Dalgarno, M. Kimura, and N. F. Lane, Phys. Rev. A 40 (1989) 2340.22. R. Walder and J. L. Franklin, Tnt. .J. Mass Spec. z Ion Phys. 36 (1980) 85.23. N. G. Adams, ,D. Smith, M. Tichy, 0. Javahery, N. D. Twiddy, and E. E. Ferguson,J. Chem. Phys. 91 (1989) 4037.24. D. K. Bohme, R. S. Hemsworth, H. W. Rundle, and H. I. Schiff, J. Chem. Phys. 58(1973) 3054; R.S. Hemsworth, H.W. Runclie, D.K. Bohrne, H.I. Schiff, B.D. Dunkin,and F.C. Fehsenfeld, .J. Chern. Phys. 59 (1973) 61; P.F. Fennelly, R.S. Hemsworth,H. I. Schiff, and D. K. Bohme, J. Chern. Phys. 58 (1973) 6405; J. D. Payzant, H. I.Schiff, and D. K. Bohrne, J. Chem. Phys. 63 (1975) 149; F. C. Fehsenfeld, J. Chem.Phys. 64 (1976) 4887; 0.1. Mackay and D.K. Bohrne, Tnt. J. Mass Spec. & Ion Phys.26 (1978) 327; S.D. Tanner, 0.1. Mackay, A. C. Hopkinson, and D. K. Bohme, mt.J. Mass Spec. & Ion Phys. 29 (1979) 153.25. 0.1. Mackay, H. I. Schiff, and D. K. Bohme, Can. J. Chern. 59 (1981) 1771; D.KBohrne, 0. I. Mackay, and H. I. Schiff, J. Chern. Phys. 73 (1980) 4976.26. Y. Ikezoe, S. Matsuoka, M. Takebe, and A.Viggiano, Gas Phase Ion—Molecule Reaction Rate Constants Through 1986 (The Mass Spectroscopy Society of Japan, Tokyo,1987).27. D. 0. Fleming, R. J. Mikula, M. Senba, D. M. Garner, and D. J. Arseneau, Chem.Phys. 82 (1983) 75.28. D.J. Arseneau, D.G. Fleming, lvi. Senba, I.D. Reid, and D.M. Garner, Can. J. Chem.66 (1988) 2018.29. D.M. Garner, D.G. Fleming, D..J. Arseneau, M. Senba, I.D. Reid, and R.J. Mikula,J. Chem. Phys. 93 (1990) 1732.30. A. C. Gonzalez, I. D. Reid, D. M. Garner, M. Senba, D. G. Fleming, D. J. Arseneau,185and J.R. Kempton, J. Chem. Phys. 91 (1989) 6164.31. E. Roduner, P.W.F. Louwrier, G.A. Brinkman, D.M. Garner, I.D. Reid, D.J. Arseneau, M. Senba, and D.G. Fleming, Ber. Bunsenges. Phys. Chem. 94 (1990) 1224.32. J. Barassin, C. Reynaud, and A. Barassin, Chem. Phys. Lett. 123 (1986) 191.33. M.F. Jarrold, A.J. lilies, and M.T. Bowers, Chem. Phys. Lett. 92 (1982) 653.34. J. E. Moryl and J. M. Farrar, J. Phys. Chem. 86 (1982) 2020; R. M. Bilotta andJ.M. Farrar, J. Phys. Chern. 85 (1981) 1515.35. N.J. Kirchner and M.T. Bowers, J. Phys. Chem. 91 (1987) 2573.36. N.G. Adams and D. Smith, Chem. Phys. Lett. 79 (1981) 563.37. P.R. Kemper, L.M. Bass, and M.T. Bowers, .J. Phys. Chem. 89 (1985) 1105; L.M.Bass, P.R. Kemper, and V.G. Anicich, J. Am. Chem. Soc. 103 (1981) 5283.38. J.R. Kempton, D.J. Arseneau, D.G. Fleming, M. Senba, A.C. Gonzalez, J.J. Pan,A. Tempeimann, and D.M. Garner, .J. Phys. Chem. 95 (1991) 7338; J.R. Kempton,M. Senba, D. J. Arseneau, A. C. Gonzalez, D. M. Garner, J. J. Pan, D. G. Fleming,P.W. Percival, J.-C. Brodovitch, and S.-K. Leung, J. Chem. Phys. 94 (1991) 1046.39. P. W. Percival, E. Roduner, and H. Fischer, Chem. Phys. 32 (1978) 353; P. W.Percival, Radiochimica Acta 26 (1979) 1; P. W. Percival, K. M. Adamson-Sharpe,J.-C. Brodovitch, S.-K. Leung, and K. E. Newman, Chem. Phys. 95 (1985) 321.40. B.F. Kiriilov, B.A. Nikol’sky, A.V. Pirogov, V.G. Storchak, V.N. Duginov, V.G.Grebennik, S. Kapusta, A. B. Lazarev, S. N. Shiiov, and V. A. Zhukov, Hyper. Int.65 (1990) 819; V.N. Duginov, V.G. Grebennik, B.F. Kiriiiov, B.A. Nikoi’sky, V.G.Oi’shevsky, A. V. Pirogov, V.Yu. Pomyakushkin, V. G. Storchak, and V. A. Zhukov,I.V. Kurchatov Institute of Atomic Energy Preprint IAE-4980/9 (1989).41. V. G. Storchak, V. N. Duginov, V. G. Grebennik, B. F. Kiriliov, V. G. Oi’shevsky,A. V. Pirogov, V.Yu. Pomyakushkin, A. N. Ponomarev, A. B. Lazarev, S. N. Shilov,and V. A. Zhukov, I. V. Kurchatov Institute of Atomic Energy Preprint IAE-5333/9(1991).42. V.G. Storchak, V.N. Duginov, B.F. Kiriiiov, A.V. Pirogov, V.G. Grebennik, A.N.Ponomarev, V. A. Zhukov, A. B. Lazarev, and S. N. Shilov, I. V. Kurchatov Instituteof Atomic Energy Preprint IAE-5214/10 (1991).43. Yu. M. Belousov, A. L. Getalov, S. P. Kruglov, L. A. Kuz’rnin, V. P. Smilga, andV.G. Storchak, Soy. Phys. .JETP 64 (Sept. 1986) 423.18644. D.G. Fleming, R.J. Mikula, and D.M. Garner, Phys. Rev. A 26 (1982) 2527; R.J.Mikula, D. G. Fleming, and D. M. Garner, Hyper. mt. 6 (1979) 379; R. J. Mikula,Ph.D. Thesis, University of British Columbia (1981).45. C.C. Anderson and S.H. Nedderrneyer, Phys. Rev. 51 (1937) 88.46. N.G. Adams and D. Smith; W. Lindinger and D. Smith, in Reactions of Small Transient Species: kinetics and energetics, A. Fontijn and M.A.A. Clyne, eds. (Academic,New York, 1983) chap. 6, 7.47. K.P. Wanczek, mt. J. Mass Spec. & Ion Proc. 95 (1989) 1.48. J. H. Futrell, in Gaseous Ion Chemistry and Mass Spectrometry, J. H. Futrell, ed.(Wiley, New York, 1986) 127.49. W. Lindinger, in Gaseous Ion Chemistry and Mass Spectrometry, J. H. Futrell, ed.(Wiley, New York, 1986) 141.50. D. Smith and N. G. Adams, in Gas Phase Ion Chemistry vol. 1, M. T. Bowers, ed.(Academic, New York, 1979) 2.51. J. H. Futrell, in Gaseous Ion Chemistry and Mass Spectrometry, J. H. Futrell, ed.(Wiley, New York, 1986) 155.52. C.F. Giese and W.B. Maier II, .1. Chem. Phys. 39 (1963) 739.53. D.L. Smith and J.H. Futrell, hit. .1. Mass Spec. Ion Phys. 14 (1974) 171.54. M.B. Comisarow and A.G. Marshall, CPL 25 (1974) 282; 26 (1974) 489.55. N. 0. Adams and D. Smith, Tnt. J. Mass Spec. & Ion Phys. 21 (1976) 349.56. B.R. Rowe, G. Dupeyrat, J.B. Marquette, D. Smith, N.G. Adams, and E.E. Ferguson, J. Chem. Phys. 80 (1984) 241; B. R. Rowe, J.-B. Marquette, and C. Rebrion,J. Chem. Soc. Far. Trans. 2 85 (1989) 1631.57. B. R. Rowe, J. B. Marquette, 0. Dupeyrat, and E. E. Ferguson, Chem. Phys. Lett.113 (1985) 403.58. O.E. Mögensen, J. Chem. Phys. 60 (1974) 998; O.E. M6gensen and P.W. PercivalRadiat. Phys. Chein. 28 (1986) 85.59. D.E. Tolliver, G.A. Kyrola, and W.H. Wing, Phys. Lev. Lett. 43 (1979) 1719.60. 5. Peyerimhoff, J. Chem. Phys. 43 (1965) 998.61. W. Kolos, Tnt. J. Quant. Chem. X (1976) 217; W. Kolos and J. M. Peek, Chem.Phys. 12 (1976) 217.18762. D.M. Bishop and L.M. Cheung, J. Mol. Spec. 75 (1979) 462.63. K. Vasudevan, Mol. Phys. 30 (1975) 437.64. R. L. Matcha and M. B. Milleur, J. Chem. Phys. 69 (1978) 3016; R. L. Matcha,M.B. Milleur, and P.F. Meier, J. Chem. Phys. 68 (1978) 4748.65. P. Rosmus and E.-A. Reinsh, Z. Naturforsch. 35A (1980) 1066; P. Rosmus, Theor.Chim. Acta 51 (1979) 359.66. G.A. Gallup, Phys. Rev. A 35 (1987) 1.67. W.P. Kraemer, A. Komornicki, and D.A. Dixon, Chem. Phys. 105 (1986) 87.68. W. G. Rich, S. M. Bobbio, R. L. Champion, and L. D. Doverspike, Phys. Rev. A 4(1971) 2253.69. F. A. Gianturco, G. Niedner, M. Noll, E. Semprini, and J. P. Toennies, Z. Phys. D 7(1987) 281; F.A Gianturco and F. Gallese, Cheni. Phys. Lett. 148 (1988) 365.70. J.W.C. Johns, J. Mo!. Spec. 106 (1984) 124.71. A. Carrington, J. Battenshaw, R. A. Kennedy, and T. P. Soft!ey, Mo!. Phys. 44(1981) 1233.72. M. Wong, P. Bernath, and T. Amano, .1. Chem. Phys. 72 (1982) 693.73. J.W. Brault and S.P. Davis, Physica Scripta25 (1982) 268; R.S. Ram, P.F. Bernath,and J.W. Brault, J. Mol. Spec. 113 (1985) 451.74. D.J. Liu, W.-C. Ho, and T. Oka, .J. Chem. Phys. 87 (1987) 2442.75. P. G. Fournier and B. Lassier-Govers, J. Physique Lettres 43 (1983) L483; P. G.Fournier and R. J. Le Roy, Chern. Phys. Lett. 110 (1984) 487.76. G. Theodorakopoulos, I.D. Petsalakis, and R..J. Buenker, J. Phys. B: At. Mo!. Phys.20 (1987) 5335.77. E. A. Gislason and G. Parlant, .J. Chein. Phys. 94 (1991) 6598.78. R. Wedlich, M.W. Karl, N. Nakanishi, and D.M. Schrader, in Positron Annihilation:Proceedings of the Seventh International Conference, New Delhi (World Scientific,Singapore, 1985) p. 408.79. M. Tichy, G. Javahery, N. D. Twiddy, and E. E. Ferguson, mt. J. Mass Spec. & IonProc. 97 (1990) 211; Chern. Phys. Lett. 144 (1988) 131.80. D.J. DeFrees and A.D. McLean, .J. Chem. Phys. 82 (1985) 333.18881. J. Tennyson and S. Miller, J. Chem. Phys. 90 (1989) 2524.82. I.D. Reid, D.M. Garner, L.Y. Lee, M. Senba, D.J. Arseneau, and D.G. Fleming, J.Chem. Phys. 86 (1987) 5578; I.D. Reid, L.Y. Lee, D.M. Garner, D.J. Arseneau, M.Senba, and D.G. Fleming, Hyp. Inter. 32 (1986) 801; D.M. Garner, D.G. Fleming,and R.J. Mikula, Chem. Phys. Lett. 121 (1985) 80.83. T. Bowen, Physics Today, July (1985) 22; A.E. Pifer, T. Bowen, and K.R. Kendall,Nuci. Instrum. Methods 135 (1976) 39.84. J.L. Beveridge, J. Doornbos, D.M. Garner, D.J. Arseneau, I.D. Reid, and M. Senba,Nuci. Instrum. Methods in Phys. Research A 240 (1985) 316.85. M. Senba, Hyper. Int. 65 (1990) 779; J. Phys. B: At. Mol. Opt. Phys. 21 (1988)3093; 22 (1989) 2027; 23 (1990) 1545.86. D.G. Fleming and M. Senba, in Atomic Physics with Positrons, J.W. Humberstonand E. A. G. Armour, eds. (Plenum, New York, 1987) p. 343.87. E. Segrè, Experimental Nuclear Physics vol. II (Wiley, New York, 1953) 166ff.88. M. Senba, D.J. Arseneau, A.C. Gonzalez, J.R. Kempton, J.J. Pan, A. Tempelmann,and D. G. Fleming, Hyper. Tnt. 63—65 (1990) 793; and paper in preparation.89. D. J. Arseneati, D. M. Garner, M. Senba, and D. G. Fleming, .1. Phys. Chem. 88(1984) 3688; D. G. Fleming, D. .1. Arseneau, D. M. Garner, M. Senba, and R. J.Mikula, Hyper. Tnt. 17—19 (1984) 655; D. .1. Arseneau, M. Sc. Thesis, University ofBritish Columbia (1984).90. D.C. Fleming, M. Senba, D..J. Arseneau, I.D. Reid, and D.M. Garner, Can. J. Chem.64 (1986) 57; D. G. Fleming, L. Y. Lee, M. Senba, D. .1. Arseneau, I. D. Reid, andD.M. Garner, Radiochimica Acta 43 (1988) 98; D.G. Fleming, Radiat. Phys. Chem.28 (1986) 115.91. J. R. Kempton, M. Senba, D. .1. Arseneau, A. C. Gonzalez, J. J. Pan, A. Tempelmann, and D. G. Fleming, Hyper. Jut. 63—65 (1990) 801; M. Senba, R. E. Turner,D. J. Arseneau, D. M. Garner, L. Y. Lee, I. D. Reid, and D. G. Fleming, Hyper. Tnt.32 (1986) 795.92. M. Senba, A.C. Gonzalez, J.R.. Kempton, D.J. Arseneau, J.J. Pan, A. Tempelmann,and D. G. Fleming, Hyper. Tnt. 63—65 (1990) 979.93. M. Senba, D. J. Arseneau, and D. G. Fleming, “Muonium Hot Atom Chemistry:theory and experiment,” in Recent Trends and Prospects in Hot Atom Chemistry,T. Matsuura, ed. (Elsevir, Kodansha, submitted 1991).18994. M.H. Yam, Ph.D. Thesis, Yale University (1979).95. A.M. Sachs and A. Sirlin, in Muon Physics vol. II, C.S. Wu and V.W. Hughes, ed.(Academic, New York, 1975).96. G. 0. Myasishcheva, Yu. V. Obukhor, V. S. Roganov, and V. 0. Firsov, Soy. Phys.JETP (Engi. Trans.) 26 (1968) 298.97. B.D. Patterson, Rev. Mod. Phys. 60 (1988) 69.98. M. Camani, E. Klempt, W. Ruegg, A. Schenck, R. Schuize, and H. Wolf, Phys. Lett.77B (1978) 326.99. D.G. Fleming, D.M. Garner, L.C. Vaz, D.C. Walker, J.H. Brewer, and K.M. Crowe,Positronium and Muonium Chemistry, H. J. Ache, ed. A. C. S. Adv. Chem. Series175 (1979) 279.100. E. Holzschuh, W. Kündig, and B. D. Patterson, Helvetica Physica Acta 54 (1981)552; Hyper. Tnt. 8 (1981) 819.101. R. H. HefFner and D. 0. Fleming, Physics Today, Dec. (1984) 30.102. D. M. Garner, Ph. D. Thesis, University of British Columbia (1979).103. D. C. Walker, Ace. Chem. Res. 18 (1985) 167; D. C. Walker, J. Phys. Chem. 85(1981) 3960; D.C. Walker, Muon and Muonium Chemistry (Cambridge University,Cambridge, 1983).104. F. James and M. Roos, MINUIT, CERN Computer 7600 Interim Programme Library,(1971).105. W. H. Press, B. P. Flannery, S. A. Teukoiski, and W. T. Vetterling, Numerical Recipies: The Art of Scientific Computing, (Cambridge University, New York, 1986).106. M. Senha, D.G. Fleming, D.J. Arseneau, D.M. Garner, and I.D. Reid, Phys. Rev. A39 (1989) 3871; M. Senba, D.M. Garner, D.J. Arseneau, and D.G. Fleming, Hyper.mt. 17—19 (1984) 703; D. 0. Fleming, R. .1. Mikula, and D. M. Garner, J. Chem.Phys. 73 (1980) 2751.107. W. J. Chesnavich, T. Sn, and M. T. Bowers, “Ion—Dipole Collisions: Recent Theoretical Advances,” in Kinetics of Ion—Molecule Reactions, P. Ausloos, ed. (Plenum,New York, 1979) 31.108. T. Su and M. T. Bowers, in Gas Phase Ion (Yhemistry vol. 1, M. T. Bowers, ed.(Academic, New York, 1979).190109. D.C. Clary, Ref. 131, p. 1613.110. G. Gioumousis and D.P. Stevenson, J. Chem. Phys. 29 (1958) 294.111. H. Eyring, J.O. Hirschfelder, and H.S. Taylor, J. Chem. Phys. 4 (1936) 479.112. E. Vogt and G.H. Wannier, Phys. Rev. 95 (1954) 1190.113. P.M. Langevin, Ann. Chim. Phys. 5 (1905) 245.114. R.C.C. Lao, R.W. Rozett, and W.S. Koski, J. Chem. Phys. 49 (1968) 4202;.115. T.F. Moran and W.H. Hamill, J. Chem. Phys. 39 (1963) 1413.116. T. Su and M.T. Bowers, J. Chem. Phys. 58 (1973) 3027; T. Su and M.T. Bowers,mt. J. Mass Spectrom. & Ion Phys. 17 (1975) 211.117. T. Su, E.C.F. Su, and M.T. Bowers, J. Chem. Phys. 69 (1978) 2243.118. T. Su and W.J. Chesnavich, J. Chem. Phys. 76 (1982) 5183.119. R.A. Barker and D.P. Ridge, J. Chem. Phys. 64 (1976) 4411.120. W.J. Chesnavich, T. Su, and M.T. Bowers, J. Chem. Phys. 72 (1980) 2641.121. D.R. Bates, Proc. Roy. Soc. A, 384 (1982) 289; D.R. Bates, Chem. Phys. Lett. 97(1983) 19; 111 (1984) 428.122. P.P. Dymerski and R.C. Duiibar, J. Chem. Phys. 57 (1972) 4049.123. T. Su and M.T. Bowers, J. Chem. Phys. 60 (1974) 4897.124. K. Sakimoto, Chem. Phys. 63 (1981) 419.125. D. P. Ridge, “Comments on Intermolecular Potentials for Polyatomic Ions and Molecules,” in Kinetics of Ion—Molecule Reactions, P. Ausloos, ed. (Plenum, New York,1979).126. F. Celli, G. Weddle, and D.P. Ridge, J. Chem. Phys. 73 (1980) 801.127. J. Turuiski and J. Niedzielski, J. Chem. Soc. Faraday Trans. 2, 84 (1988) 347.128. J.V. Dugan and J.L. Magee, J. Chem. Phys. 47 (1967) 3103; J.V. Dugan, R.W.Palmer, and J. L. Magee, Chem. Phys. Lett. 6 (1970) 158.129. T. Su, J. Chem. Phys. 88 (1988) 4102.130. W. Forst, Theory of Unimolecular Reactions, (Academic, New York, 1973).131. J. Chem. Soc. Faraday Trans. 2, 85 (1989), entire issue.191132. J. Troe, Chem. Phys. Lett. 122 (1985) 425.133. J. Troe, J. Chem. Phys. 87 (1987) 2773.134. K. Sakimoto and K. Takayanagi, J. Phys. Soc. Jpn. 48 (1980) 2076; K. Takayanagi,J. Phys. Soc. Jpn. 45 (1978) 976; K. Sakimoto, J. Phys. Soc. Jpn. 48 (1980) 1683.135. K. Sakimoto, Chem. Phys. 68 (1982) 155; K. Sakimoto, Chem. Phys. Lett. 116(1985) 86.136. K. Sakimoto, Chem. Phys. 85 (1984) 273.137. D.C. Clary, Mol. Phys. 53 (1984) 3; 54 (1985) 605.138. D.C. Clary, J. Chem. Soc. Faraday Trans. 83 (1987) 139.139. D. C. Clary, D. Smith, and N. 0. Adams, Chem. Phys. Lett. 119 (1985) 320; C.Rebrion, J. B. Marquette, B. R. Rowe, and D. C. Clary, Chem. Phys. Lett. 143(1988) 130.140. M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem. 78 (1974) 240; 79 (1975)170, 469.141. Wm.L. Morgan and D.R. Bates, Astrophys. J. 314 (1987) 817.142. L.D. Landau and E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1969) 154—158.143. N. Markovié and S. Nordholm, J. Chem. Phys. 91 (1989) 6813.144. 5. 0. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and W. 0.Mallard, J. Phys. & Chem. Ref. Data 17 (1988) Supplement 1.145. D. K. Bedford and D. Smith, Tnt. .1. Mass Spec. Ion Proc. 98 (1990) 179.146. W. Lindinger, M. McFarland, F.C. Fehsenfeld, D.L. Albritton, A.L. Schmelttekopf,and E. E. Ferguson, J. Chem. Phys. 63 (1975) 2175; W. Lindinger, Phys. Rev. A 7(1973) 328.147. N.G. Adams and D. Smith, .1. Phys. B: At. Mol. Phys. 9 (1976) 1439; N.G. Adams,D. Smith, and J.F. Paulson J. Chern. Phys. 72 (1980) 288.148. Z. Karpas, V. G. Anicich, and W. T. Huntress Jr., Chem. Phys. Lett. 59 (1978) 84.149. A.B. Rakshit and P. Warneck, J. Chem. Phys. 74 (1981) 2853.150. CRC Handbook of Chemistry and Physics, 71st ed., D. R. Lide, ed. (CRC Press, BocaRaton, 1990).151. R.E. Turner, M. Senba, and D. .J. Arseneau, Tnt. J. Quant. Chem. 29 (1986) 1493.192152. G.J. Vazquez, R.J. Buenker, and S.D. Beyeremhoff, Mol. Phys. 59 (1986) 291.153. E.E. Ferguson, J. Phys. Chem. 90 (1986) 731.154. W. Federer, W. Dobler, F. Howorka, W. Lindinger, M. Durop-Ferguson, and E. E.Ferguson, J. Chem. Phys. 83 (1985) 1032.155. R.A. Morris, A.A. Viggiano, F. Dale, J.F. Paulson, J. Chem. Phys. 88 (1988) 4772.156. M. Durup-Ferguson, H. Böhringer, D.W. Fahey, F.C. Fehsenfeld, and E.E. Ferguson,J. Chem. Phys. 81 (1984) 2657.157. P.R. Kemper and M.T. Bowers, J. Chem. Phys. 81 (1984) 2634.158. M. Konrad and F. Linder, J. Phys. B: At. Mol. Phys. 15 (1982) L405.159. D.G. Fleming, R.F. Kiefi, D.M. Garner, M. Senba, A.C. Gonzalez, J.R. Kempton,D.J. Arseneau, K. Venkateswaran, P.W. Percival, J.-C. Brodovitch, S.-K. Leung, D.Yu, and S.F.J. Cox, Hyper. mt. 63—65 (1990) 767; P.W. Percival, J.-C. Brodovitch,S.-K. Leung, D. Yu, R. F. Kiefi, D. M. Garner, D. J. Arseneau, II. G. Fleming, A. C.Gonzalez, J. R. Kempton, M. Senba, K. Venkateswaran, and S. F. J. Cox, Chem.Phys. Lett. 163 (1989) 241.160. R. F. Kiefi, S. R. Kreitzman, M. Celio, R. Keitel, 0. M. Luke, J. H. Brewer, D. R.Noakes, P. W. Percival, T. Matsuzaki, and K. Nishiyama, Phys. Rev. A 34 (1986)681; P.W. Percival, R.F. Kiefi, 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(1987) 465.161. M. Heming, E. Roduner, B.D. Patterson, W. Odermatt, J. Schneider, H. Baumeler,H. Keller, and I. M. Slavié, Chem. Phys. Lett. 128 (1986) 100; M. Heming, E.Roduner, and B. D. Patterson, Hyper. Tnt. 32 (1986) 727.162. E. Roduner, Prog. React. Kinet. 14 (1986) 1; The positive Muon as a Probe of FreeRadical Chemistry (Springer, Berlin, 1988).163. T. Sugai, T. Kondow, A. Matsushita, K. Nishiyama, and K. Nagamine, Chem. Phys.Lett. 188 (1992) 100.164. M. Senba, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) 3531; 23 (1990) 4051.165. A. A. Maryott and F. Buckley, NBS circular 537 (1953).166. Lange’s Handbook of Chemi.stry, .J. A. Dean, ed. (Mc Graw—Hill, New York, 1985).167. 0. Herzberg, Molecular Spectra and Molecular Structure III (Van Nostrand, New193York, 1966); K. P. Huber and 0. Herzberg, Molecular Spectra and Molecular Structure IV (Van Nostrand, New York, 1979).168. P. Jesson and E. L. Muetterties, Basic Chemical and Physical Data (Marcel Dekker,New York, 1969).169. Tables of Interatomic Distances and Configuration in Molecules and Ions, L. E. Sutton, ed. (The Chemical Society, London, 1958); Supplement 1956—1959, (1965).170. 0. Hvistendahl, O.W. Saastad, and E. Uggerud, mt. J. Mass Spec. & Ion Proc. 98(1990) 167.171. N.G. Adams, D.K. Bohme, and E.E. Ferguson, J. Chem. Phys. 52 (1970) 5101.172. J.D.C. Jones, D.G. Lister, D.P. Wareing, and N.D. Twiddy, J. Phys. B: At. Mol.Phys. 13 (1980) 3247.173. H.H. Michels, R.H. Hobbs, and L.A. Wright, J. Chem. Phys. 69 (1978) 5151.174. Y. Morioka, M. Ogawa, T. Matsumoto, K. Ito, K. Tanaka, and T. Hayaishi, J. Phys.B: At. Mol. Opt. Phys. 24 (1991) 791.175. L. K. Randeniya, X. K. Zeng, R. S. Smith, and M. A. Smith, J. Phys. Chem. 93(1989) 8031.176. P.A.M. van Koppen, M.F. .Jarrold, M.T. Bowers, L.M. Bass, and K.R. Jennings,J. Chem. Phys. 81 (1984) 288.177. K. Giles, N.C. Adams, and D. Smith, J. Phys. B: At. Mol. Opt. Phys. 22 (1989) 873;D. Smith and N. G. Adams, Chern. Phys. Lett. 161 (1989) 30.178. J.B. Laudenslager, W.T. Huntress, Jr., and M.T. Bowers, J. Chem. Phys. 61 (1974)4600.179. R. Marx, “Charge Transfers at Thermal Energies: Energy disposal and reactionmechanisms,” in Kinetics of Ion—Molecule Reactions, P. Ausloos, ed. (Plenum, NewYork, 1979) 103.180. M.F. Jarrold, L. Misev, and M.T. Bowers, J. Chem. Phys. 81 (1984) 4369.181. M.T. Bowers and D.D. Elleman, Chern. Phys. Lett. 16 (1972) 486.182. C.E. Hamilton, V.M. Bierbaurn, and S.R. Leone, J. Chem. Phys. 83 (1985) 601.183. Z. Herman, V. Pack, A.J. Yencha, and J. Futrell, Chem. Phys. Lett. 37 (1976) 329.184. T. Kato, J. Chem. Phys. 80 (1984) 6105.194185. B. Brehm, R. Frey, A. Küstler, and J. H. D. Eland, Tnt. J. Mass Spec. & Ion Phys.13 (1974) 251.186. F. A. Houle, S. L. Anderson, D. Cerlich, T. Turner, and Y. T. Lee, J. Chem. Phys.77 (1982) 748.187. L. Hüwel, D. R. Guyer, G.-H. Lin, and S. R. Leone, J. Chem. Phys. 81 (1984) 3520.188. R.J. Shul, R. Passarella, L.T. DiFazio, .Jr., R.G. Keesee, and A.W. Castleman, Jr.,J. Phys. Chem. 92 (1988) 4947.189. N.G. Adams, D. Smith, and E. Alge, J. Phys. B: Atom. Molec. Phys. 13 (1980) 3235.190. P. R. Kemper, M. T. Bowers, D. C. Parent, 0. Mauclaire, R. Derai, and R. Marx,J. Chem. Phys. 79 (1983) 160.191. R.D. Smith and J.H. Futrell, Tnt. J. Mass Spec. & Ion Phys. 20 (1976) 33, 43, 59, 71.192. H. Chatham, D. Hils, R. Robertson, and A. C. Gallagaher, .J. Chem. Phys. 79(1983) 1301.193. W.T. Huntress Jr., J.B. Laudenslager, and R.F. Pinizzotto Jr., mt. J. Mass Spec.& Ion Phys. 13 (1974) 331.194. J. B. Marquette, B. R. Rowe, C. Dupeyrat, C. Poissant, and C. Rebrion, Chem.Phys. Lett. 122 (1985) 431.195. I. Dotan, W. Lindinger, B. Rowe, D.W. Fahey, F.C. Fehsenfeld, and D.L. Aibritton,Chem. Phys. Lett. 72 (1980) 67.196. 0. Mauclaire, R. Derai, and R. Marx, Tnt. .1. Mass Spec. & Ion Phys. 26 (1978) 289.197. S. L. Varghese, C. Bissinger, J. M. Joyce, and R. Laubert, Phys. Rev. A31 (1984)2202; H. Tawara, At. Data and Nuci. Data Tables 22, (1978) 491; H. Tawara andA. Russek, Rev. Mod. Phys. 45, (197:3) 178.198. H. Villinger, J.H. Futrell, F. Howorka, N. Duric, and W. Lindinger, J. Chem. Phys.76 (1982) 3529.199. J.K. Kim and W.T. Huntress, Jr., J. Chem. Phys. 62 (1975) 2820.200. P.E.S. Wormer and F. deGroot, J. Chem. Phys. 90 (1989) 2344.201. W.T. Huntress and M.T. Bowers, Tnt. .J. Mass Spec. & Ion Phys. 12 (1973) 1.202. E.E. Ferguson, N.G. Adams, D. Smith, and E. Alge, J. Chem. Phys. 80 (1984) 6095.203. A.B. Rakshit, mt. J. Mass Spec. & Ion Phys. 41 (1982) 185; 36 (1980) 31.195204. A. A. Viggiano, R. A. Morris, F. Dale, J. F. Paulson, and E. E. Ferguson, J. Chem.Phys. 90 (1989) 1648.205. L. P. Theard and W. T. Huntress, J. Chem. Phys. 60 (1974) 2840.206. W. Lindinger, F. Howorka, P. Lukac, S. Kuhn, H. Villinger, E. Alge, and H. Ramler,Phys. Rev. A 23 (1981) 2319.207. D. Smith and N.G. Adams, Phys. Rev A 23 (1981) 2327.208. H. Böhringer, M. Durup-Ferguson, D.W. Fahey, F.C. Fehsenfeld, and E.E. Ferguson,J. Chem. Phys. 79 (1983) 4201.209. G. E. Quelch, Y. Xie, B. F. Yates, Y. Yamaguchi, and H. F. Schaefer III, Mol. Phys.68 (1989) 1095.210. I. Kusunoki and T. Ishikawa, J. Chern. Phys. 82 (1985) 4991.211. H. Böhringer, Chem. Phys. Lett. 122 (1985) 185.212. K. Hiraoka and P. Kebarle, J. Am. Chem. Soc. 98 (1976) 6119; Adv. Mass Spec.7B (1978) 1408.213. H. Mayne, D. G. Fleming, M. Senba, and D. J. Arseneau, work in progress.214. P. J. Estrup and R. Wolfgang, J. Am. Chem. Soc. 82 (1960) 2661; R. Wolfgang,Ann. Rev. Phys. Chem. 16 (1965) 15.215. S. Scherbarth and D. Gerlich, .1. Chem. Phys. 90 (1989) 1610.216. D.M. Sonnenfroh and S.R. Leone, .J. Chem. Phys. 90 (1989) 1677; D.C. Clary andD.M. Sonnenfroh, J. Chem. Phys. 90 (1989) 1686.217. P. Tosi, M. Ronchetti, and A. Lagan, J. Chem. Phys. 88 (1988) 4814.218. For example, H. S. Johnston, Gas Phase Reaction Rate Theory (Ronald, New York,1966).219. Yu.M. Belousov, V.N. Gorbunov, and V.P. Smilga, Hyper. mt. 65 (1990) 829.220. D. van Pijkeren, E. Boltjes, J. van Eck, and A. Niehaus, Chem. Phys. 91 (1984) 293;D. van Pijkeren, J. van Eck, and A. Niehaus, Chem. Phys. 95 (1985) 449.221. M. Durup-Ferguson, H. Böhringer, D.W. Fahey, and E.E. Ferguson, J. Chem. Phys.79 (1983) 265.222. S. C. Smith, M. J. McEwan, and R. G. Gilbert, .1. Chem. Phys. 90 (1989) 1630;J. Phys. Chem. 93 (1989) 8142.196223. R. 0. Gilbert and S. C. Smith, Theory of Unirnolecular and Recombination Reactions(Blackwell Scientific, Oxford, 1990).224. R. Patrick and D.M. Golden, J. Chem. Phys. 82 (1985) 75.225. J. Troe, Ber. Bunsenges. Phys. Chem. 87 (1983) 161; R.G. Gilbert, K. Luther, andJ. Troe, Ber. Bunsenges. Phys. Chem. 87 (1983) 169.226. L. Bass, W.J. Chesnavich, and M.T. Bowers, J. Am. Chem. Soc. 101 (1979) 5493.Appendix AINTEGRATION OF THE NUMBER OFTRANSITION STATESFor the transition state theory derivation of the Langevin rate constant, the number oftransition states was given asW(E— V) 1f211E-Vdp dd (3.31)h E01b=Oevaluated at r = r, where 75 and /‘ are the spherical-polar angles for the orbital motion.The integration proceeds as follows.To apply the Eorb limits, the momentum variables should be changed to energyaccording toU’ ______2+ 2 22mr 2nir (sin q)which describes a circle in the cartesian coordinates p vs. p,,/ sin . Introducing ( as theangle around that circle allows a change to polar coordinates according to= rV nE0th cos (A.2)= r./2rnEorb sin qsinC. (A.3)197198The Jacobian for this change of variables is mr2 sin , so rewriting (3.31) in terms ofEorb and (givesW(E— V) = f d f sin d1E-V mr2 dEorb f2 d( (A.4)= 82mr (E— v) (A.5)h28irmr 2 t4= h2(E+cq /2r )which is the result quoted as equation (3.32).The approach used by Chesnavich and Bowers [107] was to calculate the flux throughthe surface in phase space dividing reactants from products according to= fJffff 8(r — r) 6(E — H) di’ dp dçb dp ddp/h3p(E)which is not obviously the same as equation (3.29). The two can be reconciled though.First, the equation1 f27r jr p pE—VW =— J J JJ dp(, dp, dgf’ db (3.31)h Eorb=Ois multiplied by 1= f 6(r — r) di’; and the Heavyside or step function h(E — V — Eorb)is used to replace the integration limit Eorb = E — V, giving1 p2ir plr p poo pooW] J JJ J h(EVEorb)6(1r)drdpdpdcd’cb. (A.7)Ii o 0 Eorb=OThe argument E— V— Eorb can be written E—Vefl’, and the Heavyside function itselfcan be written as an integral,E-Vffh(E-V)= f 6(z) dz (A.8)where z can be anything with (in this case) units of energy; letz=E—H=E—p/2m—Vff, (A.9)199where H is the classical Hamiltonian at the transition state. Then dz = —pr/rn dpbecause both E and V are constant over the integration (they are in the limit). Thus1p2ir jlr j j pc’o pE—Vff144=—J J JJ j Jh o Eorb=O OO E—H=—c m(A.1O)Finally, the limits of the integral over dpr can be clarified by noting that the lower limitE—H = —oo implies H = oc (E is finite) or p. = oc, and the upper limit E—H = E—ffimplies H=or Pr = 0; so, reversing the limits to change the sign,12ir ir 00 00 00= hi f ffff 6(E— H) (A.11)which, when combined with equation (3.29), gives equation (A.6), the starting equationof Chesnavich and Bowers [107j.Appendix BTABULATED RESULTSIn this appendix are tabulated the useful parameters from the fits of all the data (tableB.1, beginning on the next page). Results are grouped into many series of runs sharingthe same reactant(s), moderator, and temperature. Each series begins with an identification of the gases and temperature; when there is no mention of T, room temperature isimplied. Results usually occur in pairs, giving the parameters determined for each of twoindependent histograms of data. The data are listed in approximate chronological order.The columns are: the reactant X and its concentration in 1014 moleccm3;the moderator gas M, which also identifies the reacting muonated ion, and its pressure in torr; theamplitude and relaxation rate (A1, )) of one signal, usually the slow relaxation; and thenthe other signal (A2, with the relaxations in s1. Missing (blank) entries indicatethat the corresponding signal was absent from the data, meaning the amplitude was nearzero and \ was undefined, so the data was fit without those parameters. There are theresults with only a single-component relaxation. Parameters reported without associateduncertainties had to be fixed at their expected values in order to get a reasonable fit. Thishappened whenever the “fast” relaxation became slow enough to be excessively coupledwith the “slow” relaxation.200201Table B.1. Tabulated ResultsX M A1 A2Xe Ne4.52± 0.23 1300 0.1992±0.0056 0.0082±0.0065 0.0437±0.0054 1.55±0.404.52 ± 0.23 1300 0,1993 ± 0.0064 0.0242 ± 0.0073 0.0425 ± 0.0057 1.49 ± 0.4811.50±0.60 1300 0.1454±0.0036 0.0107±0.0065 0.0809±0.0042 2.05±0.2411.50 ± 0.60 1300 0.1422 ± 0.0047 0.0230 ± 0.0077 0.0960 ± 0.0084 2.03 ± 0.332.51 ± 0.13 1300 0.2161 ± 0.0043 0.0058 ± 0.0047 0.0236 ± 0.0045 1.55 ± 0.562.51 ± 0.13 1300 0.2223 ± 0.0045 0.0312 ± 0.0049 0.0228 ± 0.0054 2.1 ± 1.17.31 ± 0.37 1300 0.1719 ± 0.0048 0.0071 ± 0.0024 0.0448 ± 0.0035 1.71 ± 0.337.31± 0.37 1300 0.1838±0.0032 0.0399±0.0049 0.0584±0.0093 4.0± 1.030.8 ± 1.5 1300 0.0873 ± 0.0029 —0.0044 ± 0.0088 0.0783 ± 0.0054 3.24 ± 0.4430.8 ± 1.5 1300 0.0961 ± 0.0033 0.049 ± 0.010 0.067 ± 0.010 4.06 ± 0.8720.1 ± 1.0 1300 0.0891 ± 0.0040 0.000 ± 0.011 0.1212 ± 0.0045 1.88 ± 0.1520.1± 1.0 1300 0.0910±0.0041 0.016± 0.011 0.1318±0.0057 2.18± 0.2020.1 ± 1.0 1300 0.1091 ± 0.0040 0.018 ± 0.010 0.0893 ± 0.0056 2.28 ± 0.2820.1± 1.0 1300 0.1122±0.0057 0.055±0.014 0.0943±0.0070 2.31±0.40Xe He21.6± 1.1 1500 0.1146±0.0028 0.0168±0.0064 0.130±0.010 4.74±0.5621.6 ± 1.1 1500 0.1085 ± 0.0040 0.057 ± 0.010 0.1350 ± 0.0093 3.71 ± 0.4510.20 ± 0.51 1500 0.1547 ± 0.0032 0.0300 ± 0.0039 0.1085 ± 0.009 1 4.12 ± 0.6810.20 ± 0.51 1500 0.1506 ± 0.0054 0.0666 ± 0.0095 0.1088 ± 0.0078 2.75 ± 0.465.10 ± 0.30 1500 0.1936 ± 0.0035 0.0308 ± 0.0049 0.0746 ± 0.0082 3.85 ± 0.915.10 ± 0.30 1500 0.1731 ± 0.0071 0.0404 ± 0.0086 0.0775 ± 0.0069 1.57 ± 0.302.90 ± 0.20 1500 0.2135 ± 0.0033 0.0202 ± 0.0042 0.0442 ± 0.0067 3.19 ± 0.872.90 ± 0.20 1500 0.2105 ± 0.0047 0.0536 ± 0.0059 0.0557 ± 0.0085 3.2 ± 1.015.20 ± 0.80 1500 0.1280 ± 0.0031 0.0372 ± 0.0065 0.1180 ± 0.0077 3.97 ± 0.4715.20 ± 0.80 1500 0.1280 ± 0.0044 0.087 ± 0.010 0.119 ± 0.011 3.99 ± 0.65NH3 He11.50 ± 0.60 1500 0.1179 ± 0.0022 0.0247 ± 0.0055 0.130 ± 0.024 9.9 ± 1.711.50±0.60 1500 0.1193±0.0028 0.0696±0.0068 0.222±0.065 16.0±3.52.80 ± 0.20 1500 0.1383 ± 0.0023 0.0213 ± 0.0046 0.135 ± 0.018 8.1 ± 1.22.80±0.20 1500 0.1396±0.0035 0.0682±0.0073 0.106±0.015 5.5± 1.21.04 ± 0.10 1500 0.2108 ± 0.0030 0.0198 ± 0.0036 0.0398 ± 0.0064 3.6 ± 1.31.04 ± 0.10 1500 0.2002 ± 0.0051 0.0440 ± 0.0057 0.0452 ± 0.0053 2.11 ± 0.615.20 ± 0.30 1500 0.1585 ± 0.0025 0.0280 ± 0.0042 0.094 ± 0.014 7.0 ± 1.45.20 ± 0.30 1500 0.1496 ± 0.0037 0.0510 ± 0.0062 0.083 ± 0.010 4.43 ± 0.91continued202Table B.1. Tabulated ResultsX M A1 ,)L A2NH3 Ne5.60 ± 0.25 1300 0.1136 ± 0.0039 0.022 ± 0.010 0.1910 ± 0.0069 2.67 ± 0.205.60 ± 0.25 1300 0.1109 ± 0.0033 0.0181 ± 0.0083 0.1715 ± 0.0043 2.41 ± 0.1410.20 ± 0.30 1300 0.0896 ± 0.0027 0.0194 ± 0.0092 0.1893 ± 0.0064 3.27 ± 0.2010.20 ± 0.30 1300 0.0849 ± 0,0021 0.0050 ± 0.0074 0.1839 ± 0.0037 3.03 ± 0.1313.50 ± 0.30 1300 0.0964 ± 0.0021 0.0122 ± 0.0074 0.196 ± 0.010 5.65 ± 0.4113.50 ± 0.30 1300 0.0958 ± 0.0018 0.0115 ± 0.0062 0.1700 ± 0.0048 4.61 ± 0.2621.60 ± 0.50 1300 0.0765 ± 0.0020 0.0087 ± 0.0087 0.198 ± 0.013 7.37 ± 0.5521.60±0.50 1300 0.0754±0.0016 0.0089±0.0072 0.1722±0.0063 6.45±0.42NH3 Ne3.40 ± 0.15 800 0.1340 ± 0.0046 0.0641 ± 0.0093 0.1115 ± 0.0072 2.72 ± 0.383.40 ± 0.15 800 0.1269 ± 0.0042 0.0391 ± 0.0072 0.0906 ± 0.0051 2.17 ± 0.273.40 ± 0.15 800 0.1164 ± 0.0048 0.040 ± 0.010 0.0910 ± 0.0055 2.05 ± 0.313.40 ± 0.15 800 0.1041 ± 0.0044 0.0201 ± 0.0082 0.0909 ± 0.0051 1.92 ± 0.266.10 ± 0.20 800 0.1131 ± 0.0035 0.0602 ± 0.0088 0.1171 ± 0.0070 3.15 ± 0.376.10 ± 0.20 800 0.1145 ± 0.0034 0.0492 ± 0.0067 0.0920 ± 0.0047 2.51 ± 0.278.20 ± 0.20 800 0.1545 ± 0.0031 0.1343 ± 0.0074 0.0823 ± 0.0086 4.62 ± 0.788.20 ± 0.20 800 0.1470 ± 0.0027 0.0574 ± 0.0051 0.0763 ± 0.0055 3.65 ± 0.4813.20± 0.26 800 0.1226±0.0028 0.1154±0.0085 0.102±0.011 5.88±0.8613.20 ± 0.26 800 0.1271 ± 0.0028 0.0535 ± 0.0059 0.0710 ± 0.0064 4.00 ± 0.66CH3F Ne19.8± 1.0 1400 0.1217±0.0035 0.0210±0.0078 0.0991±0.0052 2.99±0.3319.8 ± 1.0 1400 0.1319 ± 0.0031 0.0411 ± 0.0070 0.1010 ± 0.0068 3.44 ± 0.4539.5 ± 2.0 1400 0.0954 ± 0.0023 0.0265 ± 0.0077 0.0840 ± 0.0072 5.40 ± 0.8439.5 ± 2.0 1400 0.0988 ± 0.0028 0.0369 ± 0.0084 0.0752 ± 0.0067 3.61 ± 0.584.96 ± 0.25 1400 0.1942 ± 0.0042 0.0166 ± 0.0058 0.0607 ± 0.0050 2.34 ± 0.504.96 ± 0.25 1400 0.2081 ± 0.0032 0.0390 ± 0.0046 0.0554 ± 0.0053 2.48 ± 0.4610.35 ± 0.21 1400 0.1578 ± 0.0046 0.0300 ± 0.0079 0.0859 ± 0.0051 2.26 ± 0.3410.35 ± 0.21 1400 0.1645 ± 0.0034 0.0411 ± 0.0063 0.0979 ± 0.0056 2.83 ± 0.3527.2 ± 1.4 1400 0.1128 ± 0.0024 0.0332 ± 0.0067 0.0957 ± 0.0057 4.48 ± 0.5227.2± 1.4 1400 0.1136±0.0024 0.0329±0.0065 0.1007±0.0064 3.83± 0.42CH3F Ne11.10 ± 0.50 800 0.0793 ± 0.0036 0.025 ± 0.011 0.0812 ± 0.0053 2.72 ± 0.4211.10 ± 0.50 800 0.0792 ± 0.0042 0.023 ± 0.012 0.0791 ± 0.0059 2.27 ± 0.3622.3 ± 1.1 800 0.0526 ± 0.0027 0.038 ± 0.013 0.0797 ± 0.0068 4.57 ± 0.8522.3 ± 1.1 800 0.0550 ± 0.0028 0.050 ± 0.0 14 0.0799 ± 0.0066 4.27 ± 0.745.83 ± 0.12 800 0.1173 ± 0.0034 0.0348 ± 0.0056 0.0747 ± 0.0047 2.84 ± 0.43continued203Table B.1. Tabulated ResultsX M A1 A2 A25.83±0.12 800 0.1172±0.0039 0.0265±0.0080 0.0676±0.0050 2.09±0.3415.60 ± 0.80 800 0.0671 ± 0.0023 0.0242 ± 0.0088 0.0854 ± 0.0054 4.12 ± 0.5215.60±0.80 800 0.0724±0.0032 0.046±0.012 0.0740±0.0056 3.15±0.48N20 Ne21.5 ± 1.0 1000 0.0987 ± 0.0030 0.0084 ± 0.0078 0.0933 ± 0.0053 3.17 ± 0.3921.5 ± 1.0 1000 0.1058 ± 0.0042 0,019 ± 0.010 0.0827 ± 0.0054 2.06 ± 0.3031.9± 1.5 1225 0.1073±0.0024 0.0111±0.0066 0.1009±0.0068 5.26±0.7031.9± 1.5 1225 0.1107±0.0025 0.0270±0.0069 0.0950±0.0071 4.06±0.5213.30±0.66 1000 0.1345±0.0028 0.0154±0.0056 0.0814±0.0052 3.43±0.4613.30 ± 0.66 1000 0.1379 ± 0.0033 0.0176 ± 0.0059 0.0813 ± 0.0062 2.81 ± 0.425.70 ± 0.11 1000 0.171 ± 0.010 0.015 ± 0.010 0.0743 ± 0.0087 1.05 ± 0.205.70 ± 0.11 1000 0.1858 ± 0.0077 0.0320 ± 0.0086 0.0721 ± 0.0072 1.22 ± 0.233.420±0.068 1000 0.195±0.013 0.011±0.011 0.047±0.012 0.85±0.313.420 ± 0.068 1000 0.2050 ± 0.0074 0.0183 ± 0.0075 0.0501 ± 0.0065 1.29 ± 0.36C2H4 Ne11.00 ± 0.22 1000 0.1498 ± 0.0030 0.0156 ± 0.0056 0.0686 ± 0.0049 3.21 ± 0.5511.00 ± 0.22 1000 0.1594 ± 0.0034 0.0343 ± 0.0060 0.0572 ± 0.0054 2.69 ± 0.5521.5 ± 1.0 1000 0.1272 ± 0.0025 0.0241 ± 0.0060 0.0671 ± 0.0068 5.5 ± 1.121.5 ± 1.0 1000 0.1296 ± 0.0029 0.0210 ± 0.0065 0.0610 ± 0.0067 3.51 ± 0.775.00 ± 0.10 1000 0.1877 ± 0.0043 0.0194 ± 0.0056 0.0540 ± 0.0047 1.79 ± 0.335.00 ± 0.10 1000 0.1875 ± 0.0064 0.0197 ± 0.0069 0.0556 ± 0.0056 1.23 ± 0.3032.2 ± 1.6 870 0.0682 ± 0.0020 0.0 105 ± 0.0077 0.057 ± 0.010 7.7 ± 2.732.2± 1.6 870 0.0764±0.0025 0.0368±0.0090 0.049±0.013 7.2±3.6Kr Ne1.500 ± 0.030 1000 0.2691 ± 0.0014 0.0206 ± 0.00201.500 ± 0.030 1000 0.2804± 0.0013 0.0281 ± 0.001979.3 ± 4.0 1000 0.1275 ± 0.0092 0.013 ± 0.012 0.0536 ± 0.0087 0.90 ± 0.2179.3±4.0 1000 0.1334±0.0082 0.018± 0.011 0.0641±0.0076 0.98±0.1939.7 ± 2.0 1000 0.1741 ± 0.0077 0.0199 ± 0.0051 0.0448 ± 0.0068 1.20 ± 0.4039.7 ± 2.0 1000 0.152 ± 0.018 0.004 ± 0.018 0.074 ± 0.018 0.66 ± 0.20252. ± 12. 1000 0.0799 ± 0.0049 0.005 ± 0.012 0.0255 ± 0.0042 1.62 ± 0.38252. ± 12. 1000 0.0870 ± 0.0033 0.0260 ± 0.0092 0.0333 ± 0.0047 2.18 ± 0.58119.0 ± 6.0 1000 0.0763 ± 0.0071 0.005 ± 0.017 0.0445 ± 0.0060 1.20 ± 0.36119.0 ± 6.0 1000 0.0935 ± 0.0061 0.042 ± 0.014 0.0350 ± 0.0056 1.65 ± 0.63Xe Ne2.52 ± 0.15 1000 0.180 ± 0.026 0.028 ± 0.021 0.083 ± 0.026 0.57 ± 0.182.52 ± 0.15 1000 0.175 ± 0.050 0.033 ± 0.037 0.097 ± 0.047 0.48 ± 0.18continued204Table B.1. Tabulated ResultsX M A1 A1 A2 A20.0748 ± 0.00140.0755 ± 0.00150,2212 ± 0.00130.2300 ± 0.00130.2614± 0.00130.2792 ± 0.00130.0184 ± 0.00660.0300 ± 0.00700.0134 ± 0.00220.0229 ± 0.00210.0119 ± 0.00200.0216 ± 0.00200.215 ± 0.0400.228 ± 0.0300.122 ± 0.0120.116 ± 0.0140.1876 ± 0.00800.186 ± 0.0120.2223 ± 0.00950.200 ± 0.0100.013 ± 0.0250.023 ± 0.0190.045 ± 0.0160.039 ± 0.0200.0129 ± 0.00770.0159 ± 0.00310.0241 ± 0.00760.021.230 ± 0.0701.230 ± 0.0706.07 ± 0.366.07 ± 0.363.00 ± 0.153.00 ± 0.151.600 ± 0.0801.600 ± 0.080CH479.3 ± 4.079.3 ± 4.09.54 ± 0.199.54 ± 0.190.862 ± 0.0170.862 ± 0.017N2032.4± 1.632.4± 1.619.5± 1.019.5± 1.08.90 ± 0.188.90 ± 0.183.200 ± 0.0643.200 ± 0.064CH3F10.90 ± 0.5410.90 ± 0.5443.0 ± 2.143 .0 ± 2.15.64± 0.115.64± 0.113.000 ± 0.0603.000 ± 0.0603.870 ± 0.0773.870 ± 0.07710001000100010001000100010001000Ne100010001000100010001000He15001500150015001500150015001500He15001500150015001500150015001500149514950.030 ± 0.0400.034 ± 0.0300.131 ± 0.0120.144 ± 0.0140.0569 ± 0.00720.068 ± 0.0110.0393 ± 0.00890.0676 ± 0.00900.152 ± 0.0140.119 ± 0.0110.1028 ± 0.00630.1086 ± 0.00900.0932 ± 0.00460.1210 ± 0.00560.0754 ± 0.00720.099 ± 0.0180.0835 ± 0.00760.0905 ± 0.00740.148 ± 0.0290.076 ± 0.0220.0679 ± 0.00460.0748 ± 0.00470.058 1 ± 0.00440.0629 ± 0.00670.0658 ± 0.00500.0812 ± 0.00700.58 ± 0.300.74 ± 0.510.86 ± 0.100.78 ± 0.101.04 ± 0.210.82 ± 0.200.89 ± 0.320.34 ± 0.208.6 ± 1.17.1 ± 1.14.02 ± 0.514.11 ± 0.662.92 ± 0.342.01 ± 0.231.62 ± 0.330.90 ± 0.305.17 ± 0.853.87 ± 0.7713.3 ± 2.515.7 ± 6.43.05 ± 0.482.78 ± 0.493.00 ± 0.571.41 ± 0.321.91 ± 0.351.52 ± 0.300.1276 ± 0.00230.1407 ± 0.00260.1424 ± 0.00340.1528 ± 0.00360.1725 ± 0.00340.1626 ± 0.00500.2005 ± 0.00750.184 ± 0.0200.1870 ± 0.00230.1904 ± 0.00380.1448 ± 0.00220.1647± 0.00260.2010 ± 0.00340.2124 ± 0.00400.2192 ± 0.00320.2171 ± 0.00730.2003 ± 0.00530.1977 ± 0.00750.08 13 ± 0.00530.0747 ± 0.00700.0678 ± 0.00880.0520 ± 0.00710.0811 ± 0.00570.0304 ± 0.00760.0664 ± 0.00880.021 ± 0.0190.0958 ± 0.00430.0735 ± 0.00620.1029 ± 0.00780.1336 ± 0.00900.0878 ± 0.00490.0727 ± 0.00540.0865 ± 0.00420.0523 ± 0.00730.0851 ± 0.00650.0445 ± 0.0085continued205Table B.1. Tabulated ResultsX M A1 A2Kr He45.1 ± 2.2 1500 0.2503 ± 0.0014 0.0747 ± 0.002545.1 ± 2.2 1500 0.2657± 0.0018 0.0519 ± 0.0029482. ± 24. 1500 0.1595 ± 0.0018 0.0789 ± 0.0046482. ± 24. 1500 0.1674 ± 0.0022 0.0557 ± 0.005410.74 ± 0.50 1500 0.2667 ± 0.0017 0.0776 ± 0.002810.74 ± 0.50 1500 0.2880 ± 0.0022 0.0607 ± 0.0032NH3 Ar21.5± 1.0 600 0.0429±0.0011 0.0234±0.007521.5 ± 1.0 600 0.0481 ± 0.0011 0.0173 ± 0.0079161.0 ± 8.0 600 0.0075 ± 0.0008 0.014 ± 0.012161.0 ± 8.0 600 0.0128 ± 0.0009 0.025 ± 0.0 1480.8 ± 4.0 600 0.0217± 0.0013 0.026 ± 0.01580.8 ± 4.0 600 0.0288 ± 0.0015 0.035 ± 0.0 165.50± 0.11 600 0.0538±0.0013 0.0089±0.00765.50 ± 0.11 600 0.0611 ± 0.0014 0.0062 ± 0.0077CH4 He164.0 ± 8.0 1500 0.1356 ± 0.0019 0.0907 ± 0.0057164.0 ± 8.0 1500 0.1426 ± 0.0024 0.0732 ± 0.007016.40 ± 0.80 1500 0.2492 ± 0.0018 0.0701 ± 0.003016.40 ± 0.80 1500 0.2655 ± 0.0022 0.0496 ± 0.0035CH4 He (plus 11.1 x 10’ niolec/cm3Xe)19.8± 1.0 1500 0.1857±0.0029 0.0868±0.0055 0.087±0.016 7.3±2.019.8± 1.0 1500 0.1947±0.0036 0.0560±0.0063 0.072±0.017 6.6±2.5Xe Ne (at 172° C)7.50 ± 0.15 1400 0.073 ± 0.040 0.0 0.204 ± 0.060 0.63 ± 0.217.50 ± 0.15 1400 0.124 ± 0.040 0.0 0.180 ± 0.040 0.64 ± 0.137.50 ± 0.15 1400 0.137 ± 0.016 0.0 0.140 ± 0.015 1.03 ± 0.177.50±0.15 1400 0.194±0.018 0.0 0.117±0.016 1.12±0.2745.50 ± 0.91 1400 0.0403 ± 0.0025 0.0 0.1058 ± 0.0047 2.91 ± 0.2645.50 ± 0.91 1400 0.1066 ± 0.0041 0.0 0.0845 ± 0.0067 2.58 ± 0.3631.00 ± 0.62 1400 0.0489 ± 0.0030 0.0 0.1447 ± 0.0033 2.10 ± 0.1131.00± 0.62 1400 0.1063±0.0038 0.0 0.1383±0.0044 2.18±0.1531.00±0.62 1400 0.0573±0.0029 0.0 0.1283±0.0039 2.38±0.1731.00 ± 0.62 1400 0.1092 ± 0.004:3 0.0 0.1245 ± 0.0055 2.66 ± 0.2683.0 ± 1.7 1400 0.0338 ± 0.0028 0.0 0.0671 ± 0.0059 3.23 ± 0.6083.0± 1.7 1400 0.0897±0.0029 0.0 0.062±0.014 6.3±2.4continued206Table B.1. Tabulated ResultsX M A1 A270.0 ± 1.4 1400 0.0458 ± 0.0033 0.0 0.0853 ± 0.0064 4.29 ± 0.6870.0± 1.4 1400 0.0491±0.0023 0.0 0.0746±0.0053 4.09±0.5384.0± 1.7 1400 0.0465±0.0036 0.0 0.0657±0.0079 4.6± 1.084.0 ± 1.7 1400 0.0439 ± 0.0032 0.0 0.0693 ± 0.0057 3.18 ± 0.60119.0 ± 2.4 1400 0.0405 ± 0.0020 0.0 0.0499 ± 0.0060 5.9 ± 1.3119.0 ± 2.4 1400 0.0457 ± 0.0016 0.0 0.0517 ± 0.0078 6.7 ± 1.5NH3 Ne (at 172° C)6.00 ± 0.50 1400 0.1266 ± 0.0077 0.0 0.1722 ± 0.0070 1.51 ± 0.136.00 ± 0.50 1400 0.1332 ± 0.0046 0.0 0.1730 ± 0.0048 1.79 ± 0.123.000 ± 0.060 1400 0.140 ± 0.022 0.0 0.186 ± 0.022 0.75 ± 0.103.000 ± 0.060 1400 0.146 ± 0.019 0.0 0.181 ± 0.018 0.733 ± 0.09010.90 ± 0.22 1400 0.0913 ± 0.0050 0.0 0.1949 ± 0.0058 2.50 ± 0.1710.90 ± 0.22 1400 0.0877 ± 0.0035 0.0 0.2020 ± 0.0049 2.48 ± 0.1420.00 ± 0.40 1400 0.0749 ± 0.0027 0.0 0.1756 ± 0.0071 5.43 ± 0.4020.00±0.40 1400 0.0720±0.0021 0.0 0.1679±0.0071 4.79±0.351.500±0.030 1400 0.1992±0.0057 0.0 0.1360±0.0051 0.540±0.0901.500 ± 0.030 1400 0.1946± 0.0041 0.0 0.1424± 0.0037 0.531 ± 0.08033.00 ± 0.66 1400 0.06 14 ± 0.0019 0.0 0.1586 ± 0.0079 7.81 ± 0.6033.00 ± 0.66 1400 0.0620 ± 0.0015 0.0 0.1490 ± 0.0090 6.98 ± 0.63N20 Ne (at 172° C)33.00±0.66 1400 0.1308±0.0023 0.0 0.104±0.011 7.4± 1.233.00 ± 0.66 1400 0.1296 ± 0.0022 0.0 0.0797 ± 0.0073 5.01 ± 0.8011.00±0.22 1400 0.1906±0.0062 0.0 0.0974±0.0058 1.78±0.2611.00±0.22 1400 0.1914±0.0042 0.0 0.1036±0.0046 1.84±0.191.500 ± 0.030 1400 0.30 ± 0.12 0.0 0.043 ± 0.050 0.32 ± 0.251.500 ± 0.030 1400 0.303 ± 0.038 0.0 0.036 ± 0.050 0.34 ± 0.4021.40 ± 0.43 1400 0.1489 ± 0.0036 0.0 0.1017 ± 0.0061 3.09 ± 0.4221.40 ± 0.43 1400 0.1516 ± 0.0027 0.0 0.0972 ± 0.0056 3.39 ± 0.4056.3 ± 1.1 1400 0.0943 ± 0.0024 0.0 0.096 ± 0.016 8.7 ± 2.056.3± 1.1 1400 0.0950±0.0019 0.0 0.0714±0.0090 6.6± 1.4CH3F Ne (at 172° C)16.50 ± 0.33 1400 0.1438 ± 0.0034 0.0 0.0771 ± 0.0044 2.42 ± 0.3016.50 ± 0.33 1400 0.1888 ± 0.0039 0.0 0.0723 ± 0.0075 3.77 ± 0.765.60 ± 0.11 1400 0.1826 ± 0.0087 0.0 0.0983 ± 0.0080 1.17 ± 0.165.60 ± 0.11 1400 0.2421 ± 0.0065 0.0 0.0707 ± 0.0066 2.03 ± 0.4011.10 ± 0.22 1400 0.1665 ± 0.0042 0.0 0.0774 ± 0.0047 2.43 ± 0.3811.10±0.22 1400 0.1977±0.0056 0.0 0.0824±0.0067 2.71±0.57continued207Table B.1. Tabulated ResultsX M A1 A211.10 ± 0.22 1400 0.1825 ± 0.0039 0.0 0.0859 ± 0.0066 3.48 ± 0.5811.10±0.22 1400 0.1722±0.0040 0.0 0.0894±0.0051 2.35±0.2933.00 ± 0.66 1400 0.1299 ± 0.0029 0.0 0.0638 ± 0.0082 5.2 ± 1.233.00 ± 0.66 1400 0.1360 ± 0.0022 0.0 0.0629 ± 0.0082 6.5 ± 1.31.530 ± 0.031 1400 0.2708 ± 0.0046 0.05 0.0643 ± 0.0043 0.72 ± 0.131.530 ± 0.031 1400 0.3074± 0.0027 0.05 0.0254 ± 0.0034 1.11 ± 0.3726.40 ± 0.53 1400 0.1446 ± 0.0026 0.0 0.0555 ± 0.0066 4.6 ± 1.026.40 ± 0.53 1400 0.1409 ± 0.0021 0.0 0.0700 ± 0.0056 4.28 ± 0.6130.20 ± 0.60 1400 0.1406 ± 0.0021 0.0 0,091 ± 0.012 8.7 ± 1.730.20 ± 0.60 1400 0.1412 ± 0.0023 0.0 0.0630 ± 0.0070 5.3 ± 1.1Xe Ne (at —96° C)30.50 ± 0.61 560 0.0421 ± 0.0064 0.098 ± 0.043 0.2047 ± 0.0073 1.74 ± 0.1330.50 ± 0.61 560 0.0539 ± 0.0049 0.047 ± 0.025 0.1902 ± 0.0054 1.84 ± 0.1119.40 ± 0.39 560 0.0376 ± 0.0088 0.077 ± 0.054 0.261 ± 0.012 1.10 ± 0.1419.40 ± 0.39 560 0.0338 ± 0.0061 —0.040 ± 0.038 0.2592 ± 0.0062 1.06 ± 0.109.80 ± 0.20 570 0.010 ± 0.010 0.0 0.318 ± 0.010 0.670 ± 0.0769.80 ± 0.20 570 0.032 ± 0.012 0.0 0.295 ± 0.012 0.71 ± 0.1081.2± 1.6 565 0.0459±0.0036 0.104± 0.028 0.1056±0.0055 2.83±0.3081.2 ± 1.6 565 0.0469 ± 0.0029 0.037 ± 0.020 0.0973 ± 0.005 1 2.86 ± 0.3254.8± 1.1 565 0.0428±0.0037 0.072±0.028 0.1552±0.0055 2.58±0.1954.8± 1.1 565 0.0499±0.0035 0.050±0.022 0.1398±0.0051 2.47±0.1966.0 ± 1.3 565 0.0421 ± 0.0041 0.112 ± 0.034 0.1278 ± 0.0058 2.46 ± 0.2366.0 ± 1.3 565 0.0484± 0.0031 0.059 ± 0.021 0.1305 ± 0.0054 2.97 ± 0.2438.00 ± 0.76 550 0.0505 ± 0.0048 0.116 ± 0.030 0.1657 ± 0.0063 2.12 ± 0.1638.00 ± 0.76 550 0.0495 ± 0.0038 0.019 ± 0.022 0.1710 ± 0.0052 2.18 ± 0.14NH3 Ne (at—96° C)33.00±0.66 565 0.0756±0.0022 0.068±0.012 0.193±0.012 8.84±0.8333.00 ± 0.66 565 0.0770 ± 0.0019 0.0069 ± 0.0088 0.175 ± 0.013 8.42 ± 0.892.900 ± 0.058 570 0.086 ± 0.021 —0.002 ± 0.044 0.256 ± 0.022 0.620 ± 0.0702.900 ± 0.058 570 0.147 ± 0.015 0.042 ± 0.019 0.194 ± 0.014 0.850 ± 0.08023.10 ± 0.46 565 0.0831 ± 0.0026 0.064 ± 0.012 0.2037 ± 0.0091 5.98 ± 0.4523.10 ± 0.46 565 0.0846 ± 0.0022 0.02 14 ± 0.0093 0.1871 ± 0.0083 5.78 ± 0.4219.40 ± 0.39 565 0.0847 ± 0.0027 0.073 ± 0.012 0.2096 ± 0.0081 5.29 ± 0.3619.40 ± 0.39 565 0.0939 ± 0.0024 0.0338 ± 0.0091 0.2012 ± 0.0087 5.77 ± 0.4316.40 ± 0.33 560 0.0865 ± 0.0027 0.055 ± 0.011 0.2052 ± 0.0066 4.31 ± 0.2516.40 ± 0.33 560 0.0936 ± 0.0024 0.0 186 ± 0.0085 0.2083 ± 0.0064 4.53 ± 0.27continued208Table B.1. Tabulated ResultsX M A1 .\ A2N20 Ne (at —96° C)22.12±0.44 560 0.1568±0.0031 0.0 0.1184±0.0055 3.26±0.3222.12 ± 0.44 560 0.1525 ± 0.0030 0.0 0.1143 ± 0.0045 2.53 ± 0.2311.80 ± 0.24 560 0.1715 ± 0.0069 0.0 0.1301 ± 0.0067 1.41 ± 0.1411.80 ± 0.24 560 0.1828 ± 0.0048 0.0 0.1198 ± 0.0052 1.74 ± 0.1611.80 ± 0.24 850 0.1978 ± 0.0073 0.0296 ± 0.0089 0.1437 ± 0.0068 1.48 ± 0.1611.80 ± 0.24 850 0.1919 ± 0.0054 0.0071 ± 0.0068 0.1445 ± 0.0053 1.46 ± 0.1233.10 ± 0.66 880 0.1635 ± 0.0023 0.0292 ± 0.0047 0.1423 ± 0.0067 4.18 ± 0.3333.10 ± 0.66 880 0.1572 ± 0.0018 —0.0007 ± 0.0038 0.1422 ± 0.0046 4.17 ± 0.2633.10 ± 0.66 880 0.1633 ± 0.0033 0.0 0.1286 ± 0.0074 3.57 ± 0.3833.10±0.66 880 0.1612±0.0023 0.0 0.1427±0.0060 4.50±0.37CH3F Ne (at —96° C)33.00±0.66 565 0.1131±0.0023 0.0899±0.0082 0.0855±0.0070 5.73±0.8333.00 ± 0.66 565 0.1173 ± 0.0022 0.0416 ± 0.0068 0.0816 ± 0.0069 5.05 ± 0.8133.00 ± 0.66 835 0.1413 ± 0.0030 0.0500 ± 0.0073 0.1337 ± 0.0073 4.02 ± 0.4133.00 ± 0.66 835 0.1386 ± 0.0025 0.0225 ± 0.0058 0.1303 ± 0.0050 3.59 ± 0.303.800 ± 0.076 565 0.186 ± 0.014 0.047 ± 0.015 0.144 ± 0.013 0.93 ± 0.133.800 ± 0.076 565 0.2057 ± 0.009:3 0.032 ± 0.010 0.1272 ± 0.0087 1.07 ± 0.1211.00 ± 0.22 565 0.1661 ± 0.0040 0.0665 ± 0.0076 0.1300 ± 0.0058 2.58 ± 0.2311.00 ± 0.22 565 0.1613 ± 0.0041 0.0174 ± 0.0070 0.1381 ± 0.0050 2.22 ± 0.1922.00 ± 0.44 565 0.1343 ± 0.0028 0.0895 ± 0.0077 0.1118 ± 0.0058 4.09 ± 0.4322.00±0.44 565 0,1359±0.0023 0.0339±0.0058 0.1151±0.0053 3.89±0.3527.10 ± 0.54 565 0.1256 ± 0.0027 0.0800 ± 0.0079 0.1181 ± 0.0062 4.42 ± 0.4727.10 ± 0.54 565 0.1268 ± 0.0024 0.0260 ± 0.0063 0.1077 ± 0.0052 3.69 ± 0.3627.10 ± 0.54 850 0.1511 ± 0.0033 0.0436 ± 0.0071 0.1367 ± 0.0061 3.22 ± 0.3027.10 ± 0.54 850 0.1551 ± 0.0022 0.0274 ± 0.0048 0.1406 ± 0.0052 4.12 ± 0.2916.40± 0.33 565 0.1437±0.0035 0.0664±0.0082 0.1328±0.0063 3.49± 0.3616.40 ± 0.33 565 0.1539 ± 0.0027 0.0426 ± 0.0060 0.1243 ± 0.0064 4.17 ± 0.4316.40 ± 0.33 860 0.1732 ± 0.0037 0.0406± 0.0064 0.1514 ± 0.0056 2.60 ± 0.2116.40 ± 0.33 860 0.1753 ± 0.0026 0.0263 ± 0.0047 0.1563 ± 0.0044 3.32 ± 0.22NH3 Ne14.70 ± 0.29 1510 0.0535 ± 0.0027 0.015 ± 0.014 0.1974 ± 0.0066 3.46 ± 0.2214.70 ± 0.29 1510 0.0670 ± 0.0027 0.016 ± 0.011 0.2178 ± 0.0051 3.36 ± 0.177.40 ± 0.15 1885 0.073 ± 0.010 0.002 ± 0.014 0.201 ± 0.011 1.79 ± 0.217.40 ± 0.15 1885 0.090 ± 0.010 0.012 ± 0.011 0.228 ± 0.010 1.78 ± 0.187.40 ± 0.15 910 0.0712 ± 0.0058 0.150 ± 0.023 0.1322 ± 0.0070 2.40 ± 0.267.40 ± 0.15 910 0.0735 ± 0.0038 0.065 ± 0.013 0.1708 ± 0.0048 2.31 ± 0.147.40±0.15 1210 0.0962±0.0080 0.115±0.013 0.125±0.010 3.43±0.62continued209Table 8.1. Tabulated ResultsX M A1 A2“27.40 ± 0.15 1210 0.1162 ± 0.0077 0.0645 ± 0.0089 0. 1344 ± 0.0089 2.48 ± 0.507.40 ± 0.15 610 0.041 ± 0.016 0.182 ± 0.036 0.105 ± 0.017 2.43 ± 0.947.40 ± 0.15 610 0.039 ± 0.011 0.106 ± 0.021 0.131 ± 0.015 2.73 ± 0.737.40± 0.15 1135 0.1133±0.0018 0.0041 ± 0.0046 0.0882±0.0048 3.82±0.397.40 ± 0.15 1135 0.1447 ± 0.0017 0.0133 ± 0.0036 0.0940 ± 0.0048 4.49 ± 0.427.40 ± 0.15 1210 0,0602 ± 0.0039 —0.006 ± 0.015 0.1874 ± 0.0047 1.86 ± 0.117.40± 0.15 1210 0.0823±0.0037 0.007± 0.011 0.2040±0.0045 1.96±0.107.40 ± 0.15 1210 0.0614 ± 0.0041 0.000 ± 0.016 0.1868 ± 0.0052 1.91 ± 0.127.40 ± 0.15 1210 0.0824 ± 0.0040 0.018 ± 0.012 0.2137 ± 0.0050 2.11 ± 0.117.40 ± 0.15 1810 0.1083 ± 0.0034 0.0133 ± 0.0080 0.1565 ± 0.0053 2.37 ± 0.177.40 ± 0.15 1810 0.1316 ± 0.0027 0.0148 ± 0.0057 0.1798 ± 0.0043 2.70 ± 0.147.50 ± 0.15 1810 0.0942 ± 0.0033 —0.0006 ± 0.0087 0.1726 ± 0.0051 2.15 ± 0.137.50 ± 0.15 1810 0.1208 ± 0.0031 0.0210 ± 0.0069 0.1996 ± 0.0043 2.46 ± 0.1210.90 ± 0.22 1210 0.0537 ± 0.0036 0.016 ± 0.017 0.1749 ± 0.0057 2.54 ± 0.1910.90 ± 0.22 1210 0.0734 ± 0.0031 0.025 ± 0.012 0.2105 ± 0.0056 3.11 ± 0.1810.90 ± 0.22 1810 0.1021 ± 0.0027 0.0080 ± 0.0074 0.1613 ± 0.0067 3.32 ± 0.2510.90 ± 0.22 1810 0.1241 ± 0.0025 0.0134 ± 0.0058 0.1761 ± 0.0049 3.40 ± 0.20Xe Ne44.50 ± 0.89 1210 0.0148 ± 0.0031 0.000 ± 0.042 0.1507 ± 0.0043 2.14 ± 0.1344.50 ± 0.89 1210 0.0202 ± 0.0026 —0.014 ± 0.028 0. 1765 ± 0.0040 2.16 ± 0.1044.50 ± 0.89 1810 0.0511 ± 0.0038 —0.011 ± 0.017 0.1661 ± 0.0054 1.94± 0.1444.50± 0.89 1810 0.0640±0.0035 —0.009± 0.013 0.1806±0.0045 1.84± 0.1044.50± 0.89 2260 0.0919±0.0063 0.020± 0.017 0.1416±0.0077 1.94±0.2544.50 ± 0.89 2260 0.1079 ± 0.0055 0.003 ± 0.012 0.1488 ± 0.0064 1.69 ± 0.15CO He23.80 ± 0.48 2280 0.3172 ± 0.0010 0.0145 ± 0.001323.80 ± 0.48 2280 0.3144 ± 0.0010 0.0114 ± 0.0013279.0 ± 5.6 2280 0.2765 ± 0.0014 0.0199 ± 0.0020279.0 ± 5.6 2280 0.2754 ± 0.0014 0.0162 ± 0.0020Kr He12.80 ± 0.26 2280 0.3190 ± 0.0015 0.0189 ± 0.001912.80 ± 0.26 2280 0.3157 ± 0.0015 0.0154 ± 0.0019113.0 ± 2.3 2280 0.2889 ± 0.0016 0.0209 ± 0.0022113.0 ± 2.3 2280 0.2869 ± 0.0015 0.0211 ± 0.0022555. ± 11. 2280 0.2121 ± 0.0014 0.0260 ± 0.0028555.± 11. 2280 0.2122±0.0014 0.0239±0.0026continued210Table B.1. Tabulated ResultsX M A1 A2C2H6 He11.24 ± 0.22 2280 0.3120 ± 0.0096 0.0241 ± 0.001811.24 ± 0.22 2280 0.3042 ± 0.0048 0.0237 ± 0.0019115.3 ± 2.3 2280 0.2039 ± 0.0064 0.0261 ± 0.0038115.3 ± 2.3 2280 0.2055 ± 0.0054 0.0198 ± 0.0038H20 He1.120 ± 0.022 2280 0.3253 ± 0.0015 0.0136 ± 0.00191.120 ± 0.022 2280 0.3225 ± 0.0015 0.0116 ± 0.001910.8± 1.0 2280 0.3133±0.0012 0.0138±0.001610.8± 1.0 2280 0.3105±0.0012 0.0118±0.001679.4±4.0 2280 0.2095±0.0013 0.0317±0.002779.4 ± 4.0 2280 0.2100 ± 0.0013 0.0351 ± 0.0026CH3NO2 He2.290 ± 0.046 2280 0.2377 ± 0.0030 0.0163 ± 0.0034 0.0804 ± 0.0040 2.07 ± 0.242.290 ± 0.046 2280 0.2395 ± 0.0025 0.0170 ± 0.0030 0.0791 ± 0.0044 2.36 ± 0.264.490 ± 0.090 2280 0.2118 ± 0.0022 0.0104 ± 0.0031 0.1280 ± 0.0059 3.36 ± 0.264.490 ± 0.090 2280 0.2109 ± 0.0022 0.0101 ± 0.0031 0.1156 ± 0.0057 3.12 ± 0.251.370 ± 0.027 2280 0.2459 ± 0.0047 0.0177 ± 0.0043 0.0846 ± 0.0043 1.33 ± 0.151.370 ± 0.027 2280 0.2463 ± 0.0042 0.0169 ± 0.0040 0.0778 ± 0.0041 1.35 ± 0.146.87 ± 0.14 2280 0.2132 ± 0.0017 0.0090 ± 0.0027 0.1255 ± 0.0080 4.66 ± 0.406.87 ± 0.14 2280 0.2114 ± 0.0017 0.0075 ± 0.0026 0.1155 ± 0.0070 4.31 ± 0.34NO He9.00± 0.18 2280 0.0488±0.0090 0.152± 0.050 0.2760±0.0075 1.540±0.0809.00± 0.18 2280 0.0417±0.0069 0.100± 0.042 0.2810±0.0060 1.460±0.06622.50 ± 0.45 2280 0.0304 ± 0.0039 0.197 ± 0.051 0.3070 ± 0.0070 3.66 ± 0.1622.50 ± 0.45 2280 0.0212 ± 0.0027 0.064 ± 0.042 0.2990 ± 0.0067 3.45 ± 0.1312.00 ± 0.24 2280 0.0709 ± 0.0049 0.074 ± 0.020 0.2502 ± 0.0055 2.14 ± 0.1112.00 ± 0.24 2280 0.0704 ± 0.0045 0.071 ± 0.018 0.2501 ± 0.0057 2.18 ± 0.1135.50±0.71 2340 0.0150±0.0024 0.105±0.060 0.335±0.010 5.61±0.2535.50 ± 0.71 2340 0.0122 ± 0.0024 0.089 ± 0.080 0.307 ± 0.011 5.11 ± 0.244.490 ± 0.090 2280 0.078 ± 0.025 0.121 ± 0.060 0.244 ± 0.023 0.828 ± 0.0904.490 ± 0.090 2280 0.072 ± 0.019 0.100 ± 0.050 0.251 ± 0.018 0.853 ± 0.07367.4± 1.3 2280 0.0083±0.0019 0.1 0.270±0.018 8.69±0.5367.4± 1.3 2280 0.0070±0.0018 0.1 0.320±0.023 10.30±0.602.250 ± 0.045 2280 0.199 ± 0.012 0.034 ± 0.011 0.114± 0.011 0.89 ± 0.142.250 ± 0.045 2280 0.199 ± 0.011 0.030 ± 0.010 0.1180 ± 0.0090 0.97 ± 0.142.920 ± 0.058 2280 0.079 ± 0.020 0.03 0.242 ± 0.020 0.545 ± 0.0572.920 ± 0.058 2280 0.121 ± 0.024 0.084 ± 0.031 0.197 ± 0.023 0.654 ± 0.070continued211Table B.1. Tabulated ResultsX M A1 . A2(CH3)4Si He12.27 ± 0.25 2280 0.1237 ± 0.0026 0.0058 ± 0.0065 0.1652 ± 0.0090 3.90 ± 0.3512.27 ± 0.25 2280 0.1273 ± 0.0024 0.0203 ± 0.0060 0.198 ± 0.013 4.65 ± 0.404.490 ± 0.090 2280 0.1665 ± 0.0054 0.0390 ± 0.0080 0.1430 ± 0.0060 1.88 ± 0.184.490 ± 0.090 2280 0.1563 ± 0.0051 0.0200 ± 0.0080 0.1620 ± 0.0060 1.92 ± 0.172.470 ± 0.049 2280 0.173 ± 0.011 0.038 ± 0.013 0.150 ± 0.010 1.03 ± 0.122.470 ± 0.049 2280 0.1864 ± 0.0090 0.055 ± 0.010 0.1335 ± 0.0078 1.25 ± 0.159.12 ± 0.18 2280 0.1355 ± 0.0032 0.0320 ± 0.0073 0.1691 ± 0.0077 3.21 ± 0.269.12 ± 0.18 2280 0.1339 ± 0.0033 0.0290 ± 0.0074 0.1668 ± 0.0078 3.08 ± 0.26NH3 He2.030 ± 0.041 2280 0.128 ± 0.017 0.053 ± 0.024 0.199 ± 0.015 0.790 ± 0.0802.030 ± 0.041 2280 0.114 ± 0.015 0.031 ± 0.022 0.213 ± 0.014 0.750 ± 0.06011.10 ± 0.22 2280 0.284 ± 0.010 0.013 ± 0.010 0.0617 ± 0.0040 4.11 ± 0.1911.10 ± 0.22 2280 0.2571 ± 0.0060 0.032 ± 0.012 0.064 ± 0.012 3.81 ± 0.166.79 ± 0.14 2280 0.2635 ± 0.0068 0.021 ± 0.016 0.0703 ± 0.0038 2.49 ± 0.146.79 ± 0.14 2280 0.2431 ± 0.0058 0.046 ± 0.016 0.0740 ± 0.0042 2.31 ± 0.12CF4 lIe13.70±0.27 2280 0.2209±0.0044 0.1:339±0.0065 0.1073±0.0052 2.47±0.2713.70 ± 0.27 2280 0.2218 ± 0.0041 0.1411 ± 0.0062 0.1083 ± 0.0056 2.63 ± 0.2822.45 ± 0.45 2280 0.2057 ± 0.0035 0.1300 ± 0.0062 0. 1331 ± 0.0063 3.37 ± 0.3222.45 ± 0.45 2280 0.2135 ± 0.0031 0.1413 ± 0.0057 0.1184 ± 0.0082 4.02 ± 0.454.490 ± 0.090 2280 0.248 ± 0.013 0.105 ± 0.010 0.076 ± 0.012 0.96 ± 0.184.490 ± 0.090 2280 0.240 ± 0.045 0.1 0.079 ± 0.044 0.82 ± 0.118.97 ± 0.18 2280 0.2274 ± 0.0060 0.1219 ± 0.0073 0.1089 ± 0.0055 1.74 ± 0.198.97 ± 0.18 2280 0.2278 ± 0.006:3 0.1240 ± 0.0075 0.0978 ± 0.0057 1.62 ± 0.19Xe Ne14.42±0.29 507 0.0145±0.0026 0.05 0.144±0.023 1.16±0.3314.42±0.29 507 0.1013±0.0025 0.05 0.132±0.023 1.12±0.3314.42 ± 0.29 1000 0.0107 ± 0.0028 0.000 ± 0.064 0.2518 ± 0.0034 1.114 ± 0.03414.42 ± 0.29 1000 0.0065 ± 0.0036 0.02 ± 0.12 0.2467 ± 0.0042 1.065 ± 0.03614.42 ± 0.29 2280 0.043 ± 0.014 0.05 0.281 ± 0.011 0.808 ± 0.04614.42 ± 0.29 2280 0.0405 ± 0.0036 0.05 0.2701 ± 0.0040 0.822 ± 0.03014.52 ± 0.29 800 0.019 ± 0.010 0.13 ± 0.12 0.1868 ± 0.0092 1.110 ± 0.08114.52± 0.29 800 0.032±0.012 0.180± 0.090 0.180±0.011 1.32±0.1250.6± 1.0 800 0.0200±0.0040 0.127±0.067 0.0973±0.0061 2.63±0.3150.6 ± 1.0 800 0.0173 ± 0.0028 0.068 ± 0.054 0.1188 ± 0.0063 3.04 ± 0.2750.6± 1.0 1020 0.0095±0.0024 0.12 0.1275±0.0050 2.27±0.16continued212Table B.1. Tabulated ResultsX M A1 A2 A20.1474±0.0057 2.55±0.200.2115 ± 0.0056 1.640 ± 0.0850.2227 ± 0.0056 1.660 ± 0.085800 0.1662 ± 0.0088 0.038 ± 0.011 0.1013 ± 0.0077 1.13 ± 0.16800 0.1652± 0.0081 0.039 ± 0.010 0.0913± 0.0074 1.11 ± 0.16800 0.0112±0.0021 0.04 0.1935±0.0050 1.620±0.085800 0.017±0.012 0.16± 0.18 0.183±0.011 1.58±0.17800 0.030±0.014 0.04 0.235±0.013 0.324±0.031800 0.061 ± 0.011 0.05 0.210 ± 0.010 0.411 ± 0.035800 0.0173 ± 0.0045 0.05 0.1725 ± 0.0051 0.848 ± 0.067800 0.030 ± 0.017 0.13 ± 0.15 0.174 ± 0.017 1.08 ± 0.15Ne800 0.1192 ± 0.0085 0.0590 ± 0.0060 0.0871 ± 0,0060 1.16 ± 0.20800 0.1040 ± 0.0077 0.027 ± 0.016 0.1006 ± 0.0072 1.01 ± 0.13800 0.0609 ± 0.0042 0.001 ± 0.016 0.0741 ± 0.0043 1.54 ± 0.22800 0.0700 ± 0.0035 0.032 ± 0.0 14 0.0717 ± 0.0042 2.07 ± 0.30800 0.0341 ± 0.0016 0.040 ± 0.017 0.0380 ± 0.0080 5.3 ± 1.5800 0.0298 ± 0.0018 0.014 ± 0.019 0.0423 ± 0.0050 3.85 ± 0.83800 0.0552 ± 0.0024 0.040 ± 0.015 0.0492 ± 0.0070 3.75 ± 0.90800 0.0527 ± 0.0027 0.033 ± 0.016 0.0545 ± 0.0063 3.11 ± 0.70800 0.032 ± 0.030 0.03 0.135 ± 0.017 0.79 ± 0.60800 0.043 ± 0.025 0.03 0.117 ± 0.015 0.90 ± 0.60Ne800 0.0026 ± 0.0009 0.07 0.121 ± 0.010 5.80 ± 0.58800 0.0020±0.0018 0.05±0.49 0.1003±0.0095 5.49±0.60800 0.0103±0.0050 0.13±0.15 0.2202±0.0055 2.06±0.11800 0.0176 ± 0.0080 0.24 ± 0.16 0.2024 ± 0.0080 2.28 ± 0.17800 0.0168 ± 0.0090 0.63 ± 0.33 0.1836 ± 0.0080 4.91 ± 0.55800 0.0125 ± 0.0040 0.39 ± 0.16 0.1891 ± 0.0058 4.82 ± 0.29800 0.024±0.013 0.1 0.229±0.013 0.97±0.12800 0.043 ± 0.020 0.176 ± 0.095 0.207 ± 0.017 1.11 ± 0.12800 0.039 ± 0.025 0.07 ± 0.10 0.228 ± 0.023 0.658 ± 0.070800 0.025 ± 0.015 0.01 ± 0.10 0.239 ± 0.020 0.633 ± 0.050Ne800 0.1754 ± 0.0040 0.0505 ± 0.0060 0.0808 ± 0.0050 2.48 ± 0.42800 0.1645 ± 0.0047 0.0360 ± 0.0070 0.0793 ± 0.0047 1.67 ± 0.231020 0.0087±0.0038 0.122280 0.0377±0.0050 0.122280 0.0334±0.0049 0.12Ne50.6± 1.050.6± 1.050.6± 1.00215.26 ± 0.3115.26 ± 0.3123.90 ± 0.4823.90 ± 0.484.630 ± 0.0934.630 ± 0.09313 .50 ± 0 .2713.50 ± 0.27(CH3)4Si4.630 ± 0.0934.630 ± 0.09310.22 ± 0.2010.22 ± 0.2023.84 ± 0.4823.84 ± 0.4814.87 ± 0.3014.87 ± 0.306.88 ± 0.146.88 ± 0.14NO74.2± 1.574.2± 1.522.65 ± 0.4522.65 ± 0.4544.04 ± 0.8844.04 ± 0.8810.81 ± 0.2210.81 ± 0.226.74± 0.136.74 ± 0.13CH3NO24.520 ± 0.0904.520 ± 0.090continued213Table B.1. Tabulated ResultsX M A1 A22.250 ± 0.045 800 0.2108 ± 0.0033 0.06 0.0520 ± 0.0041 0.89 ± 0.162.250 ± 0.045 800 0.154 d: 0.032 0.0098 ± 0.0040 0.104 ± 0.029 0.55 ± 0.206.76 ± 0.14 800 0.1351 ± 0.0024 0.0175 ± 0.0054 0.0684 ± 0.0052 3.02 ± 0.456.76±0.14 800 0.1349±0.0023 0.0245±0.0053 0.0686±0.0053 2.97±0.432.250 ± 0.045 800 0.1905 ± 0.0070 0.0400 ± 0.0080 0.0736 ± 0.0063 1.21 ± 0.212.250 ± 0.045 800 0.1710 ± 0.0090 0.017 ± 0.010 0.0859 ± 0.0085 0.91 ± 0.154.490 ± 0.090 800 0.1448 ± 0.0045 0.0185 ± 0.0075 0.0934 ± 0.0048 1.70 ± 0.214.490 ± 0.090 800 0.1500 ± 0.0037 0.0268 ± 0.0067 0.0846 ± 0.0051 2.12 ± 0.3110.90 ± 0.22 800 0.1078 ± 0.0023 0.0204 ± 0.0068 0.0763 ± 0.0080 4.14 ± 0.7310.90 ± 0.22 800 0.1045 ± 0.0021 0.0185 ± 0.0065 0.0778 ± 0.0075 4.22 ± 0.64CF4 Ne11.20 ± 0.22 800 0.100 ± 0.014 0.088 ± 0.028 0.159 ± 0.012 0.98 ± 0.1111.20 ± 0.22 800 0.126 ± 0.014 0.134 ± 0.024 0.131 ± 0.012 1.16 ± 0.1722.50 ± 0.45 800 0,0868 ± 0.0043 0.099 ± 0.014 0.1597 ± 0.0041 1.94 ± 0.1322.50 ± 0.45 800 0.0924 ± 0.0051 0.119 ± 0.017 0.1426 ± 0.0047 1.89 ± 0.1447.40 ± 0.95 800 0.0760± 0.0031 0.134 ± 0.014 0.1535 ± 0.0050 3.18 ± 0.2247.40 ± 0.95 800 0.0730 ± 0.0027 0.134 ± 0.013 0.1574 ± 0.0056 3.37 ± 0.2233.90 ± 0.68 800 0.0874 ± 0.0036 0.145 ± 0.015 0.1722 ± 0.0058 3.29 ± 0.2433.90 ± 0.68 800 0.0779 ± 0.0036 0.108 ± 0.015 0.1533 ± 0.0051 2.56 ± 0.18Kr Ne22.50 ± 0.45 800 0.056 ± 0.040 0.02 0.206 ± 0.040 0.30 ± 0.1322.50 ± 0.45 800 0.078 ± 0.040 0.02 0.177 ± 0.040 0.32 ± 0.1322.50 ± 0.45 800 0.130 ± 0.045 0.02 0.103 ± 0.045 0.43 ± 0.1422.50 ± 0.45 800 0.134 ± 0.042 0.02 0.096 ± 0.046 0.47 ± 0.1544.90 ± 0.90 800 0.101 ± 0.017 0.014 ± 0.025 0.120 ± 0.016 0.573 ± 0.09044.90 ± 0.90 800 0.099 ± 0.013 0.02 0.119 ± 0.013 0.531 ± 0.08567.4± 1.3 800 0.092±0.016 0.02 0.104±0.015 0.649±0.09067.4 ± 1.3 800 0.097 ± 0.012 0.02 0.096 ± 0.011 0.70 ± 0.1090.5± 1.8 800 0.097±0.012 0.02 0.078±0.011 0.84± 0.1490.5 ± 1.8 800 0.103 ± 0.014 0.044 ± 0.024 0.062 ± 0.013 0.81 ± 0.2167.9 ± 1.4 800 0.096 ± 0.015 0.02 0.098 ± 0.012 0.64 ± 0.1067.9 ± 1.4 800 0.094 ± 0.016 0.02 0.100 ± 0.0 15 0.614 ± 0.090CO Ne22.50 ± 0.45 801 0.2529 ± 0.0011 0.0266 ± 0.001922.50 ± 0.45 801 0.2510 ± 0.0011 0.0264 ± 0.0018275.0 ± 5.5 800 0.1094 ± 0.0015 0.0254 ± 0.0055275.0 ± 5.5 800 0.1058 ± 0.0014 0.0126 ± 0.0053continued214Table B.1. Tabulated ResultsX M A1 \1 A2NO Ar22.50 ± 0.45 800 0.0002 ± 0.0032 0.05 0.0743 ± 0.0030 0.662 ± 0.07222.50 ± 0.45 800 0.0007 ± 0.0031 0.05 0.0720 ± 0.0029 0.669 ± 0.0744.520 ± 0.090 800 0.0000 ± 0.0030 0.001 0.0819 ± 0.0016 0.157 ± 0.0114.520 ± 0.090 800 0.0000 ± 0,0030 0.001 0.0795 ± 0.0015 0.166 ± 0.01150.5± 1.0 800 0.0052±0.0017 0.05 0.0674±0.0043 1.82±0.2450.5± 1.0 800 0.0010±0.0019 0.05 0.0712±0.0033 1.54±0.1736.18 ± 0.72 800 0.0005 ± 0.0018 0.05 0.0751 ± 0.0031 1.31 ± 0.1336.18 ± 0.72 800 0.0018 ± 0.0020 0.05 0.0703 ± 0.0029 1.11 ± 0.1213.50 ± 0.27 800 0.0098 ± 0.0035 0.05 0.0760 ± 0.0032 0.633 ± 0.07013.50 ± 0.27 800 0.0051 ± 0.0048 0.05 0.0750 ± 0.0042 0.492 ± 0.064CH3F Ne12.80 ± 0.26 500 0.0569 ± 0.0024 0.096 ± 0.015 0.0791 ± 0.0055 3.89 ± 0.5612.80 ± 0.26 500 0.0478 ± 0.0029 0.056 ± 0.018 0.0750 ± 0.0042 2.42 ± 0.2912.80 ± 0.26 1000 0.1216 ± 0.0033 0.0883 ± 0.0082 0.1050 ± 0.0041 2.34 ± 0.2112.80 ± 0.26 1000 0.1227 ± 0.0035 0.0892 ± 0.0086 0.1066 ± 0.0046 2.39 ± 0.2312.80 ± 0.26 1700 0.1893 ± 0.0030 0.1347 ± 0.0056 0.0884 ± 0.0047 3.01 ± 0.3212.80± 0.26 1700 0.1871±0.0036 0.1323±0.0064 0.0895±0.0049 2.64± 0.3012.80 ± 0.26 2500 0.2142 ± 0.0022 0.0312 ± 0.0031 0.0858 ± 0.0041 2.83 ± 0.2612.80 ± 0.26 2500 0.2201 ± 0.0025 0.0325 ± 0.0034 0.0741 ± 0.0048 2.77 ± 0.33CH3F He6.06 ± 0.12 1000 0.1499 ± 0.0035 0.0464 ± 0.0060 0.0777 ± 0.0058 2.48 ± 0.296.06 ± 0.12 1000 0.1522 ± 0.0033 0.0661 ± 0.0061 0.0857± 0.0063 3.03 ± 0.386.06 ± 0.12 1500 0.1950 ± 0.0031 0.0432 ± 0.0047 0.0945 ± 0.0093 3.53 ± 0.546.06± 0.12 1500 0.1911±0.0039 0.0431±0.0052 0.0843±0.0078 2.63±0.406.06 ± 0.12 2000 0.2253 ± 0.0028 0.0413 ± 0.0036 0.0790 ± 0.0084 3.70 ± 0.576.06 ± 0.12 2000 0.2219 ± 0.0021 0.0385 ± 0.0029 0.0724 ± 0.0059 3.64 ± 0.57H20 Ne (plus 6.12 x 10” molec/cm3NH3)2.030 ± 0.041 800 0.0799 ± 0.0056 0.058 ± 0.018 0.1452 ± 0.0054 1.69 ± 0.152.030 ± 0.041 800 0.0778 ± 0.0054 0.040 ± 0.018 0.1582 ± 0.0056 1.71 ± 0.1415.0 ± 1.5 800 0.1009 ± 0.0024 0.0522 ± 0.0078 0.0569 ± 0.0052 3.35 ± 0.6115.0 ± 1.5 800 0.1060 ± 0.0021 0.0591 ± 0.0069 0.0686 ± 0.0087 5.1 ± 1.04.040 ± 0.081 800 0.1003 ± 0.0032 0.0407 ± 0.0094 0.1025 ± 0.0047 2.52 ± 0.264.040 ± 0.081 800 0.1058 ± 0.0035 0.053 ± 0.010 0.1017 ± 0.0059 2.75 ± 0.357.30 ± 0.15 800 0.1071 ± 0.0025 0.0518 ± 0.0077 0.0728 ± 0.0058 3.47 ± 0.507.30 ± 0.15 800 0.1046 ± 0.0029 0.0466 ± 0.0089 0.0822 ± 0.0062 3.10 ± 0.450.00 800 0.0728 ± 0.0096 0.0836 ± 0.031 0.1746 ± 0.0080 1.37 ± 0.130.00 800 0.0565±0.0067 0.05 0.1844±0.0060 1.13±0.13continued215Table B.1. Tabulated ResultsX M A1 .\ A2C2H6 He (plus 5.08 x iO’4 molec/cm3NH3)6.35± 0.13 1500 0.1332±0.0036 0.0265±0.0067 0.1225±0.0062 3.27±0.336.35±0.13 1500 0.1344±0.0036 0.0462±0.0073 0.1141±0.0068 2.97±0.333.230 ± 0.065 1500 0.1091 ± 0.0035 0.0469 ± 0.0086 0.1542 ± 0.0070 2.98 ± 0.233.230 ± 0.065 1500 0.1075 ± 0.0038 0.053 ± 0.010 0.1443 ± 0.0065 2.54 ± 0.199.62 ± 0.19 1500 0.1400 ± 0.0031 0.0435 ± 0.0064 0.1042 ± 0.0070 3.57 ± 0.489.62 ± 0.19 1500 0.1389 ± 0.0033 0.0505 ± 0.0069 0.1025 ± 0.0076 3.63 ± 0.520.00 1500 0.0755±0.0048 0.057±0.016 0.0257±0.0061 2.11±0.110.00 1500 0.0648 ± 0.0053 0.027 ± 0.019 0.2021 ± 0.0058 1.95 ± 0.12NO Ar32.50 ± 0.65 400 0.0225 ± 0.0061 0.167 ± 0.075 0.0190 ± 0.0056 1.6 ± 1.032.50 ± 0.65 400 0.0191 ± 0.0035 0.115 ± 0.055 0.0286 ± 0.0044 2.18 ± 0.7516.30 ± 0.33 400 0.0226 ± 0.0082 0.1 0.0259 ± 0.0060 0.84 ± 0.3916.30 ± 0.33 400 0.0205 ± 0.0091 0.09 ± 0.11 0.0324± 0.0076 1.18 ± 0.5223.20±0.46 800 0.0264±0.0048 0.02 0.0448±0.0049 1.23±0.2423.20 ± 0.46 800 0.0258 ± 0.0060 0.02 0.0466 ± 0.0056 1.12 ± 0.2440.60 ± 0.81 800 0.0206 ± 0.0022 0.017 ± 0.031 0.0464 ± 0.0043 2.47 ± 0.4040.60 ± 0.81 800 0.0173 ± 0.0034 0.018 ± 0.050 0.0519 ± 0.0044 1.92 ± 0.3732.50 ± 0.65 800 0.0320 ± 0.0031 0.064 ± 0.031 0.0475 ± 0.0058 2.96 ± 0.7332.50 ± 0.65 800 0.0292 ± 0.0036 0.05 0.0465 ± 0.0045 2.17 ± 0.3716.30±0.33 800 0.0327±0.0060 0.02 0.0448±0.0060 1.05±0.5016.30 ± 0.33 800 0.034 ± 0.011 0.016 ± 0.067 0.0413 ± 0.0093 1.0 ± 1.1(C2H5)3N Ar4.060 ± 0.081 800 0.0632 ± 0.0040 0.02 0.0101 ± 0.0040 0.54 ± 0.454.060 ± 0.081 800 0.0640 ± 0.0014 0.02 0.0135 ± 0.0026 1.21 ± 0.5313.90 ± 0.28 800 0.0404 ± 0.0018 0.053 ± 0.015 0.0141 ± 0.0042 3.0 ± 1.213.90 ± 0.28 800 0.0366 ± 0.0027 0.02 0.0253 ± 0.0069 3.0 ± 1.58.23± 0.16 800 0.0512± 0.0040 0.053 ± 0.019 0.0118±0.0036 1.9± 1.68.23 ± 0.16 800 0.0477 ± 0.0024 0.010 ± 0.014 0.0153 ± 0.0037 2.05 ± 0.9221.2 ± 2.0 800 0.0364 ± 0.0020 0.022 ± 0.016 0.0162 ± 0.0034 2.2 ± 1.021.2 ± 2.0 800 0.0344 ± 0.0026 0.006 ± 0.019 0.0211 ± 0.0035 1.97 ± 0.76N20 Ne42.20 ± 0.94 800 0.0710 ± 0.0023 0.069 ± 0.011 0.070 ± 0.010 4.9 ± 1.142.20 ± 0.94 800 0,0746 ± 0.0021 0.095 ± 0.011 0.0659 ± 0.0090 4.93 ± 0.8420.12 ± 0.50 800 0.09 17 ± 0.0037 0.062 ± 0.011 0.0940 ± 0.0045 2.06 ± 0.2420.12 ± 0.50 800 0.0895 ± 0.0052 0.073 ± 0.015 0.0887 ± 0.0052 1.63 ± 0.22continued216Table B.1. Tabulated ResultsX M A1 A2Xe Ne19.00 ± 0.48 700 0.0233 ± 0.0032 0.010 ± 0.034 0.1574 ± 0.0038 1.74 ± 0.1019.00 ± 0.48 700 0.0266 ± 0.0046 0.076 ± 0.045 0.1444 ± 0.0047 1.69 ± 0.1219.00 ± 0.48 700 0.0335 ± 0.0055 0.049 ± 0.044 0.1286 ± 0.0064 1.85 * 0.2019.00 ± 0.48 700 0.0354 ± 0.0063 0.086 ± 0.050 0.1208 ± 0.0075 1.91 ± 0.2440.10 ± 0.90 700 0.0056 ± 0.0010 0.05 0.1409 ± 0.0045 2.77 ± 0.1440.10 ± 0.90 700 0.0012 ± 0.0012 0.05 0.1269 ± 0.0042 2.17 ± 0.1310.02 ± 0.30 800 0.023 ± 0.023 0.05 ± 0.13 0.252 ± 0.015 0.835 ± 0.05510.02 ± 0.30 800 0.0135 ± 0.0068 0.05 0.2240 ± 0.0044 0.891 ± 0.0343.91 ± 0.18 800 0.0890 ± 0.0061 0.04 0.1692 ± 0.0042 0.531 ± 0.0593.91 ± 0.18 800 0.0943 ± 0.0053 0.04 0.170 ± 0.013 0.488 ± 0.0492.01 ± 0.14 800 0.205 ± 0.018 0.100 ± 0.018 0.071 ± 0.021 0.37 ± 0.10105.5 ± 2.2 800 0.0020 ± 0.0015 0.05 0.047 ± 0.014 4.3 ± 1.6105.5 ± 2.2 800 0.0008 ± 0.0015 0.05 0.051 ± 0.015 5.0 ± 1.7NO Ne7.33 ± 0.25 800 0.056 ± 0.014 0.092 ± 0.045 0.198 ± 0.013 0.869 ± 0.0697.33 ± 0.25 800 0.045 ± 0.018 0.081 ± 0.068 0.205 ± 0.016 0.802 ± 0.07820.24 ± 0.50 800 0.0082 ± 0.0036 0.04 ± 0.12 0.2086 ± 0.0041 1.793 ± 0.08220.24 ± 0.50 800 0.0086 ± 0.0033 0.05 0.1994 ± 0.0041 1.741 ± 0.081NH3 Ne (plus 10.02 x i0’ molec/crn3Xe)6.01 ± 0.30 800 0.0338 ± 0.0041 0.028 ± 0.031 0.1742 ± 0.0049 1.86 ± 0.126.01 ± 0.30 800 0.0400 ± 0.0049 0.074 ± 0.034 0.1698 ± 0.0058 2.02 ± 0.1612.02 ± 0.30 800 0.0360 ± 0.0024 0.062 ± 0.02 1 0.1537 ± 0.0056 3.22 ± 0.2112.02 ± 0.30 800 0.0383 ± 0.0030 0.089 ± 0.025 0.1432 ± 0.0057 2.91 ± 0.213.01 ± 0.30 800 0.0237 ± 0.0073 0.052 ± 0.069 0.1996 ± 0.0066 1.342 ± 0.0933.01 ± 0.30 800 0.0234±0.0049 0.05 0.1983±0.0049 1.361±0.0750.00 800 0.023 ± 0.023 0.05 ± 0.13 0.252 ± 0.015 0.835 ± 0.0550.00 800 0.0135 ± 0.0068 0.05 0.2240 ± 0.0044 0.891 ± 0.0341120 Ne (plus 10.02 x i’ molec/cm3Xe)3.71 ± 0.30 800 0.0924 ± 0.0049 0.058 ± 0.014 0.0864± 0.0052 1.65 ± 0.213.71±0.30 800 0.1027±0.0054 0.095±0.015 0.0736±0.0058 1.93±0.342.00 ± 0.30 800 0.0657 ± 0.0072 0.013 ± 0.023 0.1458 ± 0.0064 1.08 ± 0.102.00 ± 0.30 800 0.0784 ± 0.0075 0.062 ± 0.022 0.1399 ± 0.0068 1.27 ± 0.126.21 ± 0.30 800 0.1028 ± 0.0045 0.040 ± 0.011 0.0726 ± 0.0048 1.69 ± 0.256.21 ± 0.30 800 0.0992 ± 0.005:3 0.043 ± 0.013 0.0698 ± 0.0054 1.51 ± 0.257.81 ± 0.30 800 0.0914 ± 0.0031 0.0605 ± 0.0091 0.0363 ± 0.0038 1.82 ± 0.437.81 ± 0.30 800 0.0876 ± 0.0036 0.061 ± 0.010 0.0389 ± 0.0038 1.67 ± 0.36continued217Table B.1. Tabulated ResultsX M A1 A2800 0.023 ± 0.023800 0.0135±0.00680.05 ± 0.13 0.252 ± 0.0150.05 0.2240 ± 0.0044(plus 20,12 x 1014 rnolec/cm3N20)0.1280± 0.00360.1240 ± 0.00600.1406 ± 0.00160.129 ± 0.0100.1352 ± 0.00200.1336 ± 0.00220.0917 ± 0.00370.0895 ± 0.00520.0770 ± 0.00800.084 ± 0.0110.0500 ± 0.00360.045 ± 0.0150.0302 ± 0.00460.0349 ± 0.00510.062 ± 0.0110.073 ± 0.015(plus 7.33 x 1014 molec/cm3NO)0.000.00Ar201.8 ± 4.0201.8 ± 4.0422.0 ± 8.4422.0 ± 8.4105.5 ± 2.1105.5 ± 2.10.000.00Ar106.4 ± 2.1106.4 ± 2.1422.0 ± 8.4422.0 ± 8.4683. ± 14.683. ± 14.0.000.00CH3NO210.48 ± 0.3110.48 ± 0.315.23 ± 0.205.23 ± 0.203.38 ± 0.173.38 ± 0.171.44 ± 0. 131.44 ± 0. 137.55 ± 0.257.55 ± 0.25CH3N5.50 ± 0.215.50 ± 0.210.82 ± 0.120.82 ± 0.12Ne800800800800800800800800Ne800800800800800800800800Ne1300130013001300130013001300130013001300Ne13001300135013500.835 ± 0.0550.891 ± 0.0342.20 ± 0.801.60 ± 0.603.6 ± 1.11.08 ± 0.653.64 ± 0.823.59 ± 0.802.06 ± 0.241.63 ± 0.220.95 ± 0.110.913 ± 0.0800.963 ± 0.0870.99 ± 0.121.14 ± 0.131.33 ± 0.190.869 ± 0.0690.802 ± 0.0782.52 ± 0.383.00 ± 0.552.16 ± 0.272.31 ± 0.321.18± 0.181.07 ± 0.180.66 ± 0.220.52 ± 0.192.33 ± 0.242.53 ± 0.310.0320 ± 0.00300.0350 ± 0.00500.0250 ± 0.00450.0243 ± 0.00900.0430 ± 0.00590.0538 ± 0.00690.0940 ± 0.00450.0887 ± 0.00520.201 ± 0.0250.216 ± 0.0160.182 ± 0.0140.171 ± 0.0190.147 ± 0.0130.135 ± 0.0130.198 ± 0.0130.205 ± 0.0160.0680 ± 0.00480.0658 ± 0.00670.0749 ± 0.00410.0764 ± 0.00510.0712 ± 0.00520.0796 ± 0.00660.052 ± 0.0150.066 ± 0.0260.0711 ± 0.00350.0723 ± 0.00450.057 ± 0.0260.040 ± 0.0170.058 ± 0.0160.066 ± 0.0210.080 ± 0.0140.096 ± 0.0150.056 ± 0.0140.045 ± 0.018(at 133° C)0.1096 ± 0.00270.1139± 0.00270.1383 ± 0.00300.1394± 0.00310.1492± 0.00570.1455 ± 0.00760.189 ± 0.0160.179 ± 0.0270.1178 ± 0.00220.1208 ± 0.0024(at 133° C)0.1773 ± 0.00220.1812 ± 0.00240.2382 ± 0.00230.2418 ± 0.00250.219 ± 0.0940.132 ± 0.0820.155 ± 0.0540.181 ± 0.0630.162 ± 0.0390.196 ± 0.0390.092 ± 0.0450.081 ± 0.068—0.0002 ± 0.00560.0142 ± 0.00560.0201 ± 0.00500.0243 ± 0.00520.0 124 ± 0.00710.0133 ± 0.00900.025 ± 0.0120.023 ± 0.0190.0057 ± 0.00410.0154 ± 0.00440.0158 ± 0.00440.0 175 ± 0.00470.0090 ± 0.00350.0184 ± 0.0038continued218Table B.1. Tabulated ResultsX M A1 A2C2H4F He (at 133° C)10.22 ± 0.30 2400 0.0926 ± 0.0065 0.067 ± 0.012 0.1546 ± 0.0059 1.51 ± 0.1310.22 ± 0.30 2400 0.0990 ± 0.0070 0.076 ± 0.012 0.1514 ± 0.0064 1.58 ± 0.165.14 ± 0.20 2400 0.085 ± 0.010 0.041 ± 0.016 0.1683 ± 0.0091 1.007 ± 0.0905.14 ± 0.20 2400 0.1074 * 0.0091 0.065 ± 0.014 0.1624 ± 0.0076 1.31 ± 0.1316.54 ± 0.43 2400 0.0915 ± 0.0044 0.0724 ± 0.0092 0.1414 ± 0.0051 2.19 ± 0.1916.54 ± 0.43 2400 0.1025 ± 0.0047 0.0895 ± 0.0095 0.1295 ± 0.0062 2.35 ± 0.2624.40 ± 0.59 2400 0.0930 ± 0.0038 0.0899 ± 0.0089 0.1253 ± 0.0056 2.82 ± 0.2924.40±0.59 2400 0.0917±0.0042 0.0839±0.0094 0.1307±0.0067 2.76±0.31CH3HO He (at 133° C)14.03 ± 0.38 2400 0.1018 ± 0.0015 0.0644 ± 0.0038 0.0968 ± 0.0091 5.88 ± 0.7614.03 ± 0.38 2400 0.0989 ± 0.0016 0.0581 ± 0.0041 0.119 ± 0.011 5.61 ± 0.659.41 ± 0.29 2400 0.1080 ± 0.0022 0.0683 ± 0.0049 0.0971 ± 0.0053 3.64 ± 0.379.41 ± 0.29 2400 0.1049 ± 0.0022 0.0673 ± 0.0048 0.1256 ± 0.0079 4.10 ± 0.427.16 ± 0.24 2400 0.1056 ± 0.0029 0.0639 ± 0.0060 0.1143 ± 0.0046 2.79 ± 0.267.16 ± 0.24 2400 0.1084 ± 0.0029 0.0753 ± 0.0060 0.1189 ± 0.0056 2.82 ± 0.281.92 ± 0.14 2400 0.1232 ± 0.0054 0.0758 ± 0.0080 0.1185± 0.0061 1.34 ± 0.101.92 ± 0.14 2400 0.1270 ± 0.0053 0.09 19 ± 0.0080 0.1278 ± 0.0057 1.54 ± 0.133.60 ± 0.17 2300 0.1259 ± 0.0031 0.0260 ± 0.0047 0.1174 ± 0.0034 1.79 ± 0.133.60 ± 0.17 2300 0.1296 ± 0.0031 0.0296 ± 0.0047 0.1223 ± 0.0042 1.97 ± 0.15C2H4 He (at 125° C)12.84 ± 0.36 2400 0.1151 ± 0.0024 0.0388 ± 0.0047 0.1311 ± 0.0053 3.26 ± 0.2512.84 ± 0.36 2400 0.1117 ± 0.0026 00283 ± 0.0050 0.1383 ± 0.0065 3.09 ± 0.257.71 ± 0.25 2400 0.1075 ± 0.0045 0.0284 ± 0.0073 0.1296 ± 0.0046 1.59 ± 0.137.71 ± 0.25 2400 0.1120 ± 0.0039 0.0306 ± 0.0066 0.1459 ± 0.0052 2.02 ± 0.165.29 ± 0.21 2400 0.1190 ± 0.0049 0.0323 ± 0.0068 0.1337 ± 0.0045 1.306 ± 0.0935.29 ± 0.21 2400 0.1121 ± 0.0060 0.0210 ± 0.0081 0.1425 ± 0.0053 1.167 ± 0.09216.34 ± 0.43 2400 0.1015 ± 0.0023 0.0348 ± 0.0051 0.1400 ± 0.0062 3.69 ± 0.2816.34 ± 0.43 2400 0.1089 ± 0.0023 0.0487 ± 0.0051 0.143 ± 0.0 10 4.48 ± 0.41CH3F He (at 125° C)20.18 ± 0.50 2400 0.1651 ± 0.0017 0.0352 ± 0.0027 0.0654 ± 0.0059 4.41 ± 0.6420.18 ± 0.50 2400 0.1732 ± 0.0015 0.0455 ± 0.0026 0.083 ± 0.012 6.8 ± 1.011.61 ± 0.33 2400 0.1814 ± 0.0026 0.0393 ± 0.0036 0.0649 ± 0.0058 3.33 ± 0.5911.61 ± 0.33 2400 0.1820 ± 0.0025 0.0401 ± 0.0035 0.0741 ± 0.0075 3.50 ± 0.555.15 ± 0.20 2400 0.1872 ± 0.0050 0.0351 ± 0.0052 0.0651 ± 0.0046 1.53 ± 0.275.15 ± 0.20 2400 0.1941 ± 0.0055 0.0453 ± 0.0056 0.0570 ± 0.0051 1.64 ± 0.372.70 ± 0.15 2400 0.212 ± 0.013 0.049 ± 0.010 0.054 ± 0.013 0.68 ± 0.182.70 ± 0.15 2400 0.197 ± 0.011 0.0357 ± 0.0086 0.064 ± 0.010 0.86 ± 0.23continued219Table B.1. Tabulated ResultsX M A1‘1 A2CH3F He (at —145° C)10.53 ± 0.31 800 0.1588 ± 0.0020 0.0528 ± 0.0035 0.0958 ± 0.0067 4.36 ± 0.4710.53 ± 0.31 800 0.1612 ± 0.0020 0.0574 ± 0.0036 0.122 ± 0.011 5.46 ± 0.594.17 ± 0.18 800 0.1685 ± 0.0033 0.0533 ± 0.0044 0.0916 ± 0.0041 2.15 ± 0.224.17 ± 0.18 800 0.1724 ± 0.0031 0.0572 ± 0.0043 0.0994 ± 0.0061 2.34 ± 0.267.81 ± 0.26 800 0.1602 ± 0.0019 0.0678 ± 0.0033 0.1042 ± 0.0050 3.72 ± 0.327.81 ± 0.26 800 0.1597 ± 0.0022 0.0654 ± 0.0036 0.1019 ± 0.0058 3.11 ± 0.342.20 ± 0.14 800 0.164 ± 0.012 0.058 ± 0.010 0.106 ± 0.010 0,784 ± 0.0792.20 ± 0.14 800 0.1799 ± 0.0084 0.0762 ± 0.0080 0.0849 ± 0.0080 1.10 ± 0.202.66 ± 0.15 800 0.1722 ± 0.0059 0.0673 ± 0.0061 0.0945 ± 0.0056 1.14 ± 0.122.66± 0.15 800 0.1727±0.0059 0.0670±0.0062 0.0943±0.0054 1.27±0.15Xe Ne (at —156° C)11.97 ± 0.34 370 0.003 ± 0.016 0.047 ± 0.063 0.213 ± 0.015 0.764 ± 0.07011.97 ± 0.34 370 —0.014 ± 0.020 —0.04 ± 0.10 0.226 ± 0.019 0.655 ± 0.08911.97 ± 0.34 370 —0.010 ± 0.011 0.008 ± 0.053 0.225 ± 0.010 0.708 ± 0.04411.97 ± 0.34 370 0.006 ± 0.014 0.066 ± 0.047 0.209 ± 0.013 0.795 ± 0.06526.05 ± 0.62 370 —0.0009 ± 0.0064 0.073 ± 0.036 0.198 1 ± 0.0063 1.48 ± 0.1026.05 ± 0.62 370 0.0041 ± 0.0064 0.099 ± 0.031 0.1839 ± 0.0069 1.54 ± 0.1252.0± 1.1 370 —0.0145±0.0030 0.008± 0.025 0.1326±0.0057 1.97±0.1652.0 ± 1.1 370 —0.0018 ± 0.0030 0.087 ± 0.020 0.145 ± 0.010 2.61 ± 0.256.94 ± 0.24 370 0.0 0.0 0.2691 ± 0.0020 0.3965 ± 0.00616.94 ± 0.24 370 0.0 0.0 0.2771 ± 0.0021 0.4039 ± 0.00633.94± 0.18 370 0.0 0.0 0.2894±0.0019 0.2652±0.00383.94 ± 0.18 370 0.0 0.0 0.2920 ± 0.0018 0.2622 ± 0.00383.94 ± 0.18 1000 0.0 0.0 0.3167 ± 0.0016 0.1903 ± 0.00273.94 ± 0.18 1000 0.0 0.0 0.3293 ± 0.0019 0.1998 ± 0.00316.94 ± 0.24 1000 0.0227 ± 0.0079 0.04 0.2465 ± 0.0068 0.355 ± 0.0206.94 ± 0.24 1000 0.0263 ± 0.0079 0.04 0.2479 ± 0.0064 0.382 ± 0.02452.0± 1.1 1000 0.0396±0.0072 0.088±0.019 0.1767±0.0063 1.263±0.09252.0± 1.1 1000 0.0376±0.0077 0.083±0.019 0.1794±0.0072 1.218±0.09326.05 ± 0.62 1000 0.0003 ± 0.0039 0.03 0.279 ± 0.021 0.615 ± 0.05726.05 ± 0.62 1000 0.0102 ± 0.0044 0.05 0.263 ± 0.017 0.666 ± 0.06411.97 ± 0.34 1000 0.045 ± 0.017 —0.007 ± 0.028 0.213 ± 0.016 0.566 ± 0.05111.97 ± 0.34 1000 0.029 ± 0.023 —0.016 ± 0.038 0.221 ± 0.022 0.488 ± 0.056C2H4F He (at —125° C)7.24 ± 0.24 830 0.1240 ± 0.0035 0.1569 ± 0.0080 0.1592± 0.0064 3.64 ± 0.297.24 ± 0.24 830 0.1282 ± 0.0040 0.1572 ± 0.0086 0.1472 ± 0.0080 3.49 ± 0.362.54 ± 0.15 830 0.1504 ± 0.0058 0.1327 ± 0.0084 0.1197 ± 0.0055 1.85 ± 0.19continued220Table B.1. Tabulated ResultsX M A1 .A1 A22.54 ± 0.15 830 0.1500 ± 0.0063 0.1337 ± 0.0092 0.1243 ± 0.0061 1.83 * 0.191.04 ± 0.12 830 0.170± 0.011 0.136 ± 0.012 0.098 ± 0.010 1.19 ± 0.171.04 ± 0.12 830 0.163 ± 0.012 0.123 ± 0.013 0.102 ± 0.011 1.10 ± 0.174.15 ± 0.18 830 0.1363 ± 0.0049 0.1334 ± 0.0081 0.1269 ± 0.0048 1.94 ± 0.164.15 ± 0.18 830 0.1455 ± 0.0049 0.1432 ± 0.0081 0.1281 ± 0.0053 2.18 ± 0.205.89 ± 0.22 830 0.1232 ± 0.0033 0.1393 ± 0.0071 0.1482 * 0.0049 3.01 ± 0.215.89 ± 0.22 830 0.1231 ± 0.0038 0.1408 ± 0.0078 0.1538 ± 0.0061 2.96 ± 0.24C2H4F He (at —65° C)3.11 ± 0.16 1330 0.1727 ± 0.0056 0.1436 ± 0.0075 0.0955 ± 0.0053 1.79 ± 0.203.11 ± 0.16 1330 0.1555± 0.0077 0.127 ± 0.010 0.1103 ± 0.0068 1.49 ± 0.187.22 ± 0.24 1330 0.1439 ± 0.0042 0.1533 ± 0.0077 0.1189 ± 0.0049 2.54 ± 0.247.22 ± 0.24 1330 0.1454 ± 0.0046 0.1538 ± 0.0081 0.1256 ± 0.0061 2.73 ± 0.3010.99 ± 0.32 1330 0.1232 ± 0.0041 0.1510 ± 0.0082 0.1236 ± 0.0045 2.53 ± 0.2210.99± 0.32 1330 0.1285±0.0040 0.1592±0.0082 0.1297±0.0062 3.12±0.342.10 ± 0.14 1330 0.1629 ± 0.0086 0.126 ± 0.010 0.1079 ± 0.0076 1.31 ± 0.162.10 ± 0.14 1330 0.1701 ± 0.0093 0.135 ± 0.010 0.0947 ± 0.0079 1.38 ± 0.219.61 ± 0.29 1330 0.1328 ± 0.0033 0.1486 ± 0.0068 0.1298 ± 0.0046 2.97 ± 0.249.61 ± 0.29 1330 0.1394 ± 0.0035 0.1659 ± 0.0071 0.1411 ± 0.0076 3.79 ± 0.3912.69 ± 0.35 1330 0.1261 ± 0.0035 0.1560 ± 0.0076 0.1251 ± 0.0050 2.99 ± 0.2612.69 ± 0.35 1330 0.1304 ± 0.0034 0.1608 ± 0.0074 0.1275 ± 0.0071 3.51 ± 0.3615.98 ± 0.42 1330 0.1100 ± 0.0038 0.1525 ± 0.0084 0.1163 ± 0.0044 2.74 ± 0.2615.98 ± 0.42 1330 0.1128 ± 0.0038 0.1553 ± 0.0084 0.1259 ± 0.0059 3.12 ± 0.325.39 ± 0.21 1330 0.1460 ± 0.0082 0.144 ± 0.012 0.1096 ± 0.0069 1.79 ± 0.265.39± 0.21 1330 0.1423±0.0079 0.140± 0.012 0.1178±0.0072 1.87±0.2710.48 ± 0.31 1330 0.1267 ± 0.0032 0.1589 ± 0.0068 0.1339 ± 0.0042 3.06 ± 0.2310.48 ± 0.31 1330 0.1261 ± 0.0030 0.1542 ± 0.0065 0.1379 ± 0.0055 3.17 ± 0.24CH3HO He (at —110° C)5.70 ± 0.21 960 0.1358 ± 0.0028 0.0584 ± 0.0050 0.1045 ± 0.0052 3.01 ± 0.305.70±0.21 960 0.1359±0.0027 0.0656±0.0050 0.1200±0.0073 3.47±0.332.70 ± 0.15 960 0.1376 ± 0.0029 0.0673 ± 0.0053 0.1199 ± 0.0053 2.98 ± 0.272.70 ± 0.15 960 0.1276 ± 0.0043 0.0615 ± 0.0069 0.0973 ± 0.0052 1.87 ± 0.219.35 ± 0.29 960 0.1301 ± 0.0015 0.0525 ± 0.0033 0.132 ± 0.011 7.23 ± 0.739.35 ± 0.29 960 0.1291 ± 0.0017 0.0592 ± 0.0036 0.127 ± 0.014 6.93 ± 0.811.56 ± 0.13 960 0.151 ± 0.010 0.056 ± 0.010 0.1070± 0.0091 0.97± 0.131.56 ± 0.13 960 0.160 ± 0.012 0.067 ± 0.012 0.095 ± 0.010 1.02 ± 0.194.44 ± 0.19 960 0.1421 ± 0.0031 0.0524 ± 0.0054 0.1230 ± 0.0060 3.01 ± 0.284.44 ± 0.19 960 0.1461 ± 0.0036 0.0579 ± 0.0059 0.1109 ± 0.0079 3.00 ± 0.40continued221Table B.1. Tabulated ResultsX M A1 A2C2HF5.0±0.15.0±0.113.2 ± 0.213.2 ± 0.222.8 ± 0.322.8 ± 0.317.3 ± 0.317.3 ± 0.3NO22.57 ± 0.5422.57 ± 0.5445.1 ± 1.045.1 ± 1.069.1 ± 1.569.1 ± 1.591.6± 1.9He170017001700170017001700170017008008008008008008008000.050.050.00.00.00.00.050.0554 ± 0.00280.0520 ± 0.003 10.0560 ± 0.00260.04 12 ± 0.00230.0427 ± 0.00650.059 1 ± 0.00790.0543 ± 0.00372.88 ± 0.752.84 ± 0.844.3 ± 1.43.4 ± 0.74.95 ± 0.866.72 ± 1.76.68 ± 1.34.12 ± 0.650.77 ± 0.110.64 ± 0.100.878 ± 0.0640.633 ± 0.0570.91 ± 0.211.35 ± 0.231.64 ± 0.24CH3F15.26 ± 0.4115.26 ± 0.4110.27 ± 0.3110.27 ± 0.316.94± 0.246.94 ± 0.244.23 ± 0.184.23 ± 0.1817.47 ± 0.4517.47 ± 0.45CH3NO22.31 ± 0.502.31 ± 0.5011.05 ± 0.6411.05 ± 0.645.34 ± 0.425.34 ± 0.428.27 ± 0.548.27 ± 0.54Ne370370370370370370370370370370Ne7407407407407407407407400.0543 ± 0.0064 0.1030 ± 0.0055 3.35 ± 0.340.0583 ± 0.0072 0.0993 ± 0.0069 3.25 ± 0.410.0511 ± 0.0060 0.1133 ± 0.0040 2.48 ± 0.200.0641 ± 0.0058 0.1158 ± 0.0056 3.02 ± 0.270.0550 ± 0.0088 0.1077 ± 0.0053 1.46 ± 0.150.0625 ± 0.0081 0.1142 ± 0.0058 1.74 ± 0.180.0648 ± 0.0093 0.1041 ± 0.0061 1.25 ± 0.140.054 ± 0.011 0.1107 ± 0.0077 1.07 ± 0.130.0845 ± 0.0060 0.1054 ± 0.0083 4.92 ± 0.590.0844 ± 0.0065 0.1031 ± 0.0083 4.15 ± 0.470.054 ± 0.029 0.051 ± 0.052 0.50 ± 0.310.020 ± 0.037 0.107 ± 0.046 0.31 ± 0.250.0242 ± 0.0040 0.0726 ± 0.0047 3.39 ± 0.440.0283 ± 0.0037 0.0938 ± 0.0069 4.21 ± 0.440.0192 ± 0.0052 0.0898 ± 0.0039 1.90 ± 0.200.0304 ± 0.0057 0.0751 ± 0.0047 1.80 ± 0.250.0241 ± 0.0036 0.0808 ± 0.0036 2.58 ± 0.220.0268 ± 0.0040 0.0793 ± 0.0046 2.60 ± 0.28(at —157° C)0.0800 ± 0.00250.0789 ± 0.00290.0908 ± 0.00270.0954 ± 0.00260.1035 ± 0.00520.1072 ± 0.00460.1236 ± 0.00680.1129± 0.00880.0929 ± 0.00220.0888 ± 0.0024(at —50° C)0.188 ± 0.0530.134 ± 0.0700.1100± 0.00200.1137± 0.00170.1278 ± 0.00340,1372 ± 0.00390.1255 ± 0.00200.1288 ± 0.00230.0059 ± 0.00270.0015 ± 0.00320.00.00.00.0—0.0042 ± 0.0024N2Table B.1. Tabulated ResultsX M A1 A291.6± 1.9 800 —0.0031±0.0012 0.05 0.0479±0.0032 1.77±0.22129.1 ± 2.7 800 0.0 0.0 0.0653 ± 0.0043 2.52 ± 0.23129.1 ± 2.7 800 0.0 0.0 0.0415 ± 0.0035 1.98 ± 0.21222

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0060595/manifest

Comment

Related Items