The positive muon and μSR spectroscopy: powerful tools for investigating the structure and dynamics...

Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2013, 109, 65--112 65

This journal is © The Royal Society of Chemistry 2013

Cite this: Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2013, 109, 65–112

The positive muon and lSR spectroscopy:powerful tools for investigating the structureand dynamics of free radicals and spin probesin complex systems

Iain McKenzie*ab

DOI: 10.1039/c3pc90005c

The positive muon (m+) can be incorporated into free radicals where it acts as a probe of

the structure and dynamics. The muoniated radicals are characterized by a series of

magnetic resonance techniques known as mSR for muon spin rotation, resonance and

relaxation spectroscopy. In this review it is shown how mSR can be used to obtain

information about the structure, dynamics, and local environments of transient radicals

in solids like zeolites, in solution or even in exotic solvents like supercritical water. It will

also be demonstrated that muoniated radicals can be used as probes in complex systems,

such as rod-like and discotic liquid crystals, bilayers and polymers, where they have

advantages over traditional spin labelling.

1 Introduction

Radicals are atoms or molecules with one or more unpaired electrons, whichfrequently makes them highly reactive. Radicals are often short-lived intermediatesin chemical reactions and it is necessary to determine their structure, dynamicsand reactivity in order to fully understand the reactions in which they are involved.The high reactivity of free radicals makes them difficult to study with mostconventional spectroscopic techniques. The main method for studying transientradicals is electron paramagnetic resonance (EPR)1 and in recent years thistechnique has been used to investigate the local structure and dynamics ofparamagnetic centres in biological samples2 and to determine the distancesbetween stable nitroxide spin labels in proteins.3

There are alternative magnetic resonance techniques for studying radicals thatare based on using the positive muon, m+, a short-lived radioactive particle, as aspin probe. These techniques are collectively known as mSR, which stands for

a Centre for Molecular and Materials Science, TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. Canada.

E-mail: [email protected]; Fax: +1 604 222 1074; Tel: +1 604 222 7386b Department of Chemistry, Simon Fraser University, 8888 University Drive, Burnaby, B.C. Canada

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66 Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2013, 109, 65--112


muon spin rotation, resonance, and relaxation and have been used extensively toprobe a wide range of phenomena in condensed matter physics, such as magneticordering, superconductivity and defects in semiconductors.4–7 The positive muonbehaves like a light proton and can be substituted into molecules with an ensemblepolarization of nearly 100% and its short lifetime makes it convenient for studyingfast chemical reactions and short-lived species. The use of the positive muon as aprobe of free radical chemistry has been reviewed severely times,8–12 but the focus ofthis field has changed considerably over the last decade, which is why the currentreview was thought to be timely. The goal of this article is to familiarize chemistswith the mSR technique and to show that it can provide unique information aboutthe structure and dynamics of free radicals and how these radicals can be used asprobes in complex systems like zeolites or liquid crystals. I will not tackle the closely-related subject of muonium spectroscopy or discuss muonium kinetics studies.

1.1 Muons, muonium and muoniated radicals

The central character in this review is the positive muon (m+), which is anelementary particle with a mass one ninth that of the proton, a spin of 1/2 anda magnetic moment (mm) 3.183 times larger than that of a proton (mp). Positivemuons are produced by the decay of positive pions (lifetime = 26 ns), which are inturn produced by the bombardment of a high density and low Z material, such asgraphite, with high-energy protons.

p+ - m+ + nm (1)

The neutrino in the pion decay has negative helicity (i.e. angular momentumantiparallel to the linear momentum), and because of conservation of linear andangular momentum the muon is bound to also have negative helicity. By momentumselection, muon beams can be produced with high spin polarization. Muons arepresent in cosmic radiation but high intensity beams of spin-polarized muonsrequired for spectroscopic studies are only available at four facilities throughout theworld (TRIUMF, Canada; ISIS, UK; Paul Scherrer Institute, Switzerland; J-PARC, Japan).There are several types of muon beam that are in common use. In beamlines known asdecay channels the muons are collected from the decay of p+ in flight. A beamlinetuned to the momentum range 60–120 MeV c�1 collects ‘‘backward-decay’’ muonswith an average polarization of typically 80%, which is parallel to their flight direction.The corresponding particle energy is about 40 MeV, and the stopping range in matteris about 1 g cm�2. The most frequently used type of beamline is known as a ‘‘surfacemuon’’ beamline and is tuned to a momentum of 28 MeV c�1, which selects muonscoming only from the decay of pions that are at rest near the surface of the productiontarget. The surface muon beam has a polarization very close to 100%. The muonenergy is 4 MeV, and the stopping range is 0.15 � 0.01 g cm�3, which corresponds apenetration depth of about 0.2 mm in copper, 1.5 mm in water, or 1 m in He gas atSTP. Recently a low energy muon beamline has been developed at the Paul ScherrerInstitute. The beam energy can be varied between 1 and 30 keV and is used for studiesof thin films, multi-layers and near surface regions (depths r300 nm).13,14

The polarization of the ensemble of m+, which is independent of temperature ormagnetic field, is incredibly important as it contributes significantly to thesensitivity of the magnetic resonance techniques based on m+. There is no need

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to first create spin coherence using a high frequency preparation pulse, so thetime resolution is significantly increased over that of more conventional techni-ques. The B100% polarization of a beam of muons should be contrasted with thespin polarization in typical magnetic resonance experiments, which depends onthe temperature and magnetic field and is B3 � 10�5 for protons at 300 K and9.4 T. A unique aspect of muon spectroscopy is that experiments can beperformed at low temperatures and in zero magnetic field.

TRIUMF and PSI are quasi-continuous muon sources while ISIS and J-PARC arepulsed sources. The two types of beam structures permit complementary experi-mental conditions, with continuous beams being suited best for fast processesand high precession frequencies, and pulsed beams being superior for slowprocesses, which benefit from the low background in between the pulses, andexternal stimuli such as RF or laser excitation.

Another key aspect of the muon spectroscopic techniques is that the polariza-tion of an ensemble of m+ can be monitored by measuring the asymmetry in themuon’s radioactive decay. The muon decays to a positron (e+) and two neutrinos.

m+ - e+ + ne + �nm (2)

with a lifetime of 2.197 ms. The decay of the positive muon violates parity and as aresult, the positron is emitted preferentially along the axis of the muon’s spin. Thisprovides a convenient means of determining the direction of the muon’s spin.

Muons can be implanted into solid, liquid, or gaseous samples. The implantedmuons initially have very high energy but are slowed down to thermal energies on thenanosecond timescale with the polarization being mostly conserved. The finalchemical environment of the muon depends on the chemical properties of thematerial in which it has been implanted. A fraction of the implanted muons will endup in diamagnetic chemical environments, as ‘‘bare’’ muons, solvated muons, orsubstituted for the proton of a diamagnetic molecule (such as in MuOH or C6H11Mu).The short lifetime of the muon limits the spectral resolution to B70 kHz so it is notpossible to resolve chemical shifts and distinguish between muons in differentdiamagnetic environments. Another fraction of muons can pick up an electronduring the slowing down process and form muonium (Mu = [m+, e+]), a one-electronatom with the positive muon as the nucleus. The fraction of muons forming Mudepends strongly on the material and its physical state, ranging from 0 in liquid CCl4(ref. 15) to 1.0 in gaseous Kr.16 The Mu fraction in water depends strongly on thephase, temperature and pressure, and is 0.196 � 0.03 for liquid water at ambienttemperature and pressure17 and increases to 0.801 � 0.050 at 673 K and 245 bar.18

The main chemical properties of muonium, protium (H), deuterium (D), andtritium (T) are listed in Table 1. The chemical properties of Mu are very similar to

Table 1 Chemical properties of muonium, protium, deuterium, and tritium

Property Mu H D T

Mass (mH) 0.1131 1.000 1.998 2.993Reduced mass (me) 0.9952 0.9995 0.9997 0.9998Ionization potential (eV) 13.539 13.598 13.601 13.602Bohr radius (pm) 53.17 52.94 52.93 52.93AX (MHz) 4463 1420 218 1516

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those of the hydrogen isotopes, so it is common to refer to it as a light isotope ofhydrogen, even though the conventional definition of isotopes are atoms thathave nuclei with the same number of protons but a different number of neutrons.The mass of Mu is B1/9H but the chemical properties of Mu are similar to thoseof the other hydrogen isotopes because the m+ is much heavier than the electronand the chemical properties depend on the reduced mass. Positronium is also aone-electron atom, but is not considered a hydrogen isotope because its reducedmass and chemical properties are very different from that of H or D.

There is a hyperfine interaction between the unpaired electron and nuclearspins with the strength of this interaction, the isotropic hyperfine couplingconstant (hfcc), proportional to the unpaired spin density at the nucleus,|c(0)|2, and the nuclear gyromagnetic ratio. The hfcc (in megahertz) is given by

AX ¼2m03h

gebegXbXjcð0Þj2 (3)

where ge is the free electron g factor, be is the Bohr magneton, gX is nuclear g factor,and bX is the nuclear magneton. In the condensed phase, the hfcc of Mu and theother hydrogen isotopes are altered by the interaction between the atom and theneighbouring molecules.19,20 Comparisons between different isotopes are made byconsidering the reduced hfcc, A0X, which is given by multiplying the hfcc by the ratioof the proton and nuclear magnetic moments A0X ¼ gpAX=gX

� �, where X = m, p or d.

Muonium, like the other hydrogen isotopes,21 is extremely reactive due to itsunpaired electron. Mu can react with organic compounds by abstracting an atomsuch as H, which generates a radical and the MuH molecule, which is indistinguish-able from other diamagnetic muon states. Another reaction pathway for moleculescontaining double or triple bonds is for Mu to add to the multiple bond, whichproduces a radical (called a muoniated radical†) where it takes the position of aproton attached to an atom next to the radical centre (i.e., b-position), in the sameway as a deuteron could (Fig. 1). The addition reaction to CQC bonds is typicallytwo orders of magnitude faster than the abstraction reaction, so addition dominateswhen a CQC bond is present. The spin polarization of an ensemble of muons canbe preserved during the formation of the muoniated radicals, which makes themuon a polarized spin label in the radical. There are several advantages of muonlabelling compared with traditional labelling using nitroxides or other persistentradicals and characterization using EPR spectroscopy:� The muoniated radicals are produced in situ.� The production of the muoniated radicals does not require a complicated mixture

of harsh chemicals like Fenton’s reagent or by radiolysis with electrons or g-rayswhere multiple reactive species are produced and scavengers must be added.� There are at given instant only a few muoniated radicals in the sample. This

means that bimolecular termination reactions can be ignored, so kinetics arealways of first or pseudo-first order and radicals can be studied under conditionswhere they are highly mobile.� All of the muoniated radicals reported to date, with a notable exception

discussed below, are the primary radical products of the Mu addition reaction.

† Older literature use the term muonated radical. This has been discontinued as ‘‘muonation’’ is nowdefined to be the equivalent of protonation.22


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This is advantageous as EPR studies of transient radicals are frequently compli-cated by simultaneous detection of secondary and later products.

1.2 Muon spin spectroscopy

mSR stands for muon spin rotation, relaxation and resonance, which are acollection of spectroscopic techniques that are extremely useful for characterizingtransient free radicals. These techniques involve injecting a beam of spin-polarized positive muons into a sample and detecting the positron produced bythe decay of each muon. The three techniques frequently used for characterizingmuoniated radicals are transverse field muon spin rotation (TF-mSR), avoidedlevel crossing muon spin resonance (ALC-mSR) and longitudinal field muon spinrelaxation (LF-mSR) and they will be described in detail in this section.

1.2.1 Transverse field muon spin rotation. The basic experimental geometry isshown in Fig. 2. The muon is injected into the sample with its spin perpendicularto the external magnetic field. Each incident muon passes through a muoncounter, which starts a fast electronic clock that is subsequently stopped by thedetection of the corresponding decay positron in one of the positron detectors.Events where multiple muons or positrons are detected within the sample duringa time window of several microseconds are discarded. The data are displayed as ahistogram of the number of decay positrons detected in a given direction as afunction of the lifetime of the corresponding muon and resembles the freeinduction decay that follows a p/2 pulse in nuclear magnetic resonance (NMR).The histograms have the form

N(t) = N0e�t/tm [1 + S(t)] + Bg, (4)

Fig. 1 Formation of muoniated radicals; (a) alkyl radical; (b) cyclohexadienyl radical; (c) muonoxy-alkylradical; (d) vinyl radical.


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where S(t) represents the mSR signal and Bg is a time-independent background term.The frequency spectrum is obtained by Fourier transforming S(t) which has the form:

SðtÞ ¼Xi

ARie�lRi

t cosðoRitþ fRi

Þ þ ADe�lDt cosðoDtþ fDÞ; (5)

where lRi¼ 1=TRi

2 is the transverse relaxation rate for a particular radical precessionfrequency oRi

, with experimental amplitude ARiand initial phase fRi

; and AD, lD, oD,and fD are the corresponding characteristics of the diamagnetic precession signal.

The radical precession frequencies are due to transitions between spin statesand are frequently labelled according to the spin states involved. The magneticmoment of the unpaired electron couples to the magnetic moments of the muonand any other nuclei, resulting in a multitude of spin states. In low magneticfields, the muon polarization is distributed over many transition frequencies,which makes detection of muoniated radicals difficult or impossible.23 In highmagnetic fields, where the Zeeman energy is much larger than the hyperfineinteractions, the frequency spectrum is considerably simplified, and two radicalfrequencies are observed at the same frequencies as observed in electron-nucleardouble resonance spectroscopy (Fig. 3). The radical frequencies are given by:

n12 ¼ nmid �1

2Am (6)

n43 ¼ nmid þ1

2Am (7)

where

nmid ¼1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2

m þ ne þ nDð Þ2q

� ne þ nD� �

(8)

and ne and nD are the electron and muon Larmor frequencies. In high fields, where(ne + nD)2

c Am2, nmid E nD, the precession frequency of muons in diamagnetic

environments (nD = 13.55 kHz G�1). Am (in units of frequency) is calculated from thedifference in the two precession frequencies and the isotropic muon hfcc of anorganic radical is typically between a few megahertz and approximately 700 MHz.11

Fig. 2 Schematic of the TF-mSR experimental geometry.


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In some cases the higher frequency radical precession frequency is not observed dueto the time resolution of the mSR spectrometer and Am must be determined from thelower frequency radical precession frequency and nmid. In situations where nmid isless than Am/2 one of the radical frequencies will be negative, which can bedistinguished from positive frequencies by using two sets of orthogonal positrondetectors. It is good practice to perform TF-mSR measurements at more than onemagnetic field and confirm that the radical frequencies shift appropriately.

The reaction rate of a muoniated radical with some reacting species, S, can bedetermined from the damping of the radical precession signal, which is related tothe linewidth of the TF-mSR line. The damping rate (lRi

) is related to the pseudo-first-order rate constant for the reaction of the radical with S, kR, by

lRi= l0 + kR[S] (9)

where l0 is the damping in the absence of chemical reaction, which is frequently dueto magnetic field inhomogeneity, and [S] is the concentration of the reacting species.

The muoniated radical must be formed promptly in order for the muon spinpolarization to be transferred from the Mu precursor to the radical. A slower formationreduces polarization because of dephasing of the precessing muons in the transversefield. The fraction of spin polarization transferred to a radical (PR) may be calculatedfor the general case. In the high-field limit, the corresponding expression simplifies to

PR ¼lMu

2

lMu2 þ do2

(10)

where lMu equals kMu, the rate constant for Mu addition to the parent compound,times the concentration of the parent compound and do is the difference betweenthe muon precession frequencies in Mu and in the radical. The minimumconcentration at which a radical can be observed in a TF-mSR spectrum dependson the muonium reaction rate, but is typically 0.1–0.5 M for kMu on the order of3.7 � 109 M�1 s�1, which is the rate of addition of Mu to benzene in n-hexane.25

Fig. 3 Two Fourier transformed transverse field muon spin rotation spectra at 2.9 and 14.5 kG of the0.5 M Na2C4O4 solution at 298 K. The peaks due to diamagnetic muons (nD) have been truncated to betterdisplay the peaks due to the muoniated 1,2-dicarboxyvinyl radical dianion (�O2C–(Mu)CQC–CO2

�), withAm = 493.8 � 0.2 MHz. In the spectrum at 2.9 kG the n12 line is negative while in the 14.5 kG spectrum then12 line is negative and the n43 line is not observed due to the time resolution of the spectrometer.24


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1.2.2 Avoided level crossing muon spin resonance. The ALC-mSR techniqueinvolves measuring the time-integrated asymmetry of the muon decay as a functionof a magnetic field applied parallel to the initial direction of the muon spin. Incontrast to TF-mSR, there is no restriction on the number of muons in the sample atone time so it is possible to run at a much higher incident muon rate and thedephasing problem of TF-mSR does not apply to longitudinal fields so it is possible toobserve species using ALC-mSR that are formed within B1 ms of muon implantation.This makes it possible to study samples with a low concentration of the precursormolecule (on the order of millimolar for molecules with aromatic functional groups).

The setup for an ALC-mSR experiment is shown in Fig. 4. It is possible to runboth TF-mSR and ALC-mSR experiments on the same apparatus, merely byrepositioning the counters and changing the beam polarization. The asymmetryparameter, A(t), is defined as

A ¼ nB � nF

nB þ nF(11)

where nF is the total number of positrons detected in the forward counters and nB

is the total number of positrons detected in the backward counters, and isproportional to the time-averaged muon polarization, Pz. The time-integratedasymmetry is measured as the magnetic field is scanned in a series of small steps.

In high magnetic fields the eigenstates of the radical can be approximated bypure Zeeman states, so there is no evolution of the muon’s spin with time and theasymmetry is independent of the magnetic field. At specific values of the appliedmagnetic field nearly degenerate pairs of spin states can be mixed through theisotropic and anisotropic components of the hyperfine interaction. The muonpolarization oscillates between the two mixing states and this leads to a loss oftime-integrated asymmetry (Fig. 5). There are three types of resonances, which arecharacterized by the selection rule D|M| = 0,�1 and�2, where M is the sum of themz quantum numbers of the muon, electron and proton spins. The resonancesare referred to as D0, D1 and D2 resonances, respectively. The D2 resonance isextremely weak and is rarely observed. There can be only one D1 resonance foreach type of radical but there can be as many D0 resonances as there are nuclei

Fig. 4 Schematic of the ALC-mSR or LF-mSR experimental geometry. ALC-mSR is a time-integraltechnique while LF-mSR is a time-differential technique.


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with I 4 0 in the radical, although in practice the number of observable D0

resonances is less than the maximum as many of these nuclei can have smallhfccs, which results in very small resonance amplitudes (Fig. 6).

The D0 resonance is due to mixing between spin states that have the sameelectron spin but opposite muon and proton spins and is observed for muoniatedradicals in the solid, liquid or gas phases (Fig. 5). The D0 resonance field dependson both the muon hfcc, Am, and the nuclear hfcc, AX, and is given by:

BD0res ¼

1

2

Am � AX

gm � gX� Am þ AX

ge

" #(12)

where gm, gX and ge are the muon, nuclear and electron gyromagnetic ratios,respectively. The amplitude of the D0 resonance is given by

Amplitude / P0zoLCR

2

leff2 þ oLCR2

(13)

Fig. 5 High-field energy level diagram for a three-spin system of an electron e, positive muon m, andproton k. Muon avoided level crossing resonances occur when states with opposite muon spins becomenear-degenerate in energy, allowing the system to oscillate between them.

Fig. 6 ALC-mSR spectrum of the Mu13C60 radical in decalin solution at 293 K. The approximately differentialshape of each resonance is a consequence of the square-wave field modulation used to suppress systematicdeviations of the baseline due to beam fluctuations. Resonances due to 13C atoms with positive hfccs arefound below B13.2 kG while those with negative hfccs are found above this field.26


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where oLCR is the frequency at resonance and leff is the effective relaxation rate(muon decay rate plus any additional relaxation contribution).

oLCR ¼ffiffifficp

pAmAX

geBD0res

(14)

and c is the number of magnetically equivalent nuclei with I = 1/2 at resonance.The D1 resonance field is given by:

BD1res ¼

1

2

Am

gm� Am

ge

" #(15)

The D1 resonance arises from mixing between spin states with the same electronand nuclear spins but different muon spin directions (Fig. 5). These spin statesare only mixed in the presence of anisotropy, so the presence of a D1 resonancecan be considered to be diagnostic of a frozen state or of anisotropic motion. Theresonances are averaged out by isotropic motion on a critical time scale given bythe inverse of the hyperfine anisotropy (typically B50 ns for a cyclohexadienyl-type radical).

The D1 resonance is suitable for studying anisotropic reorientational motion ofradicals in single crystals as well as in polycrystalline or amorphous states. Thelineshape of the D1 resonance is extremely sensitive to and characteristic ofthe type of reorientational motion that the muoniated radical is undergoing. Thetime-integrated polarization as a function of field for a radical with an axiallysymmetric muon dipolar tensor ([DJ

m, D>m , D>

m ] where D>m = �0.5DJ

m) is given by:

PzðBÞ ¼ 1� P0zpq

2 sin y dy

ðl=2pÞ2 þ q2 þ ðnm � nmÞ2(16)

where P0z is the muon polarization at time zero of the species of interest, y is the

angle between the unique axis of the hyperfine tensor and the applied magneticfield, l is the rate for a reaction to a state outside resonance,

q ¼ 3

2D?m sin y cos y: (17)

and

n0m ¼1

2Aiso

m þD?m 1� 3 cos2 y� �h i

(18)

This is a Lorentzian resonance with a half width at half maximum of q2 + (l/2p)2

and a position and amplitude that depends on the orientation of the moleculewith respect to the magnetic field. The powder pattern is obtained by integrationof eqn (16) over y and the resonance has a characteristic asymmetry depending onthe sign of the dipolar coupling constant when l is small. The resonance isasymmetric with the cusp falling on the low-field side when the parameters Aiso

m ispositive and D>

m is negative and is on the high-field side when both Aisom and

D>m are positive. The asymmetry arises from the greater weight of orientations

with y = 901 over those with y = 01. The resonance becomes more symmetric withincreased relaxation (i.e. when l c 2pq).

The shape of resonances in ALC-mSR is sensitive to the motion of the radicaland can be used to determine whether the motion of the radical is anisotropic and,


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in some cases, what is the preferred reorientation axis, as motion modulates thedipolar coupling constant. An axial hyperfine tensor arises if the radical isundergoing rapid uniaxial rotation. Fig. 7 shows the simulated spectra of themuoniated cyclohexadienyl radical around the D1 and the D0 methylene protonresonances for different types of reorientational motion. The static hyperfinetensor of the C6H6Mu radical is expected to be similar to that of the muoniated2,3,5,6-tetramethylcyclohexadienyl radical, which was determined from an angledependent TF-mSR study of a single crystal of durene.27 There is a large positiveprincipal component of 8.15 MHz oriented approximately along the C–Mu bond,at an angle of 251 with respect to the molecular plane. This is nearly balanced by anegative out-of-plane component of �9.05 MHz, leaving only a small in-planeprincipal component of +0.9 MHz. Fast uniaxial rotation about an axisperpendicular to the molecular plane results in D>

m = +3.4 MHz while fastuniaxial rotation about the long axis of the radical results in D>

m = �2.9 MHz.28

The different types of motion will reverse the high- and low-field sides and changethe width of the D1 resonance, so it is possible to determine the preferredrotational axis from the line shape of the powder spectra. An axial lineshapewith a further reduced width would indicate more extensive averaging bytumbling or wobbling motion superimposed on the rapid uniaxial rotation.

The effect of more complex processes on the ALC lineshapes must be simulatednumerically. Kreitzman and Roduner used numerical simulations to investigate theeffect of rotational diffusion, chemical reaction and electron spin relaxation on theshape of D1 and D0 resonances.29 This can work can now be easily reproduced usingthe program ‘‘Quantum’’ written by Lord.30 Tregenna-Piggott et al. used Monte Carlomethods to simulate ALC line shapes for different types of molecular motion.31

Fig. 7 Simulated powder pattern for the D1 resonance of the cyclohexadienyl type radical in the staticcase (top), for fast rotation about two different axes (middle two entries), and for fast isotropic motion.28


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1.2.3 Longitudinal field muon spin relaxation. Longitudinal field muon spinrelaxation (LF-mSR) can be used to probe dynamics in free radicals. Experimentallythe technique is the same as ALC-mSR, except that the time dependence of thepolarization is monitored rather than integrated as in ALC-mSR. ALC-mSR and LF-mSRspectra can be obtained simultaneously using high field spectrometers at pulsedfacilities.32 The theory of the LF-mSR has been developed by Cox and variouscoworkers for a m+–e� system.33,34 The overall spin relaxation is due to transitionsbetween electron and muon spin states that are mixed by the hyperfine coupling.Motional perturbations induce transitions between the mixed spin-states, withdifferent selection rules and dependencies on magnetic field according tomechanism. The time dependence of the muon polarization is given by:

PzðtÞ ¼ 2X4i¼1

niðtÞ i Izj jih i2 (19)

where |ii are the four spin states of the m+–e� system. In principle the time evolution ofPz(t) is the superposition of three exponential terms, but in practice it is indistinguish-able from a single exponential or represented by a stretched exponential model.

A alternative way to determine the muon hfcc of Mu or muoniated radicals is bydetermining the magnetic field dependence of the initial relaxing asymmetry inwhat is known as a ‘‘repolarization’’ curve. This method has a long historyand remains an important technique for characterizing unknown systems, andparticularly for those with state-to-state transitions or dynamical properties andhas been useful as well in characterizing anisotropic muon environments in thesolid state. The basis of the technique will be described for the case of isotropicMu and is equally valid for the case of a muoniated radical with no nuclear spins.Mu is produced from 100% spin polarized m+(am) but the electrons in the stoppingmedium are unpolarized, so Mu forms equally in an initial ensemble of two spinstates, |amaei and |ambei. The |amaei state is an eigenstate of the spin Hamiltonian,but the |ambei state is a superposition of two eigenstates and as such oscillates intime, evolving into the |bmaei state at the muon hfcc frequency of Am = 4463 MHz.

In zero or weak fields the |ambei state appears to be completely depolarized,given the time resolution of most detection systems. Increasing the strength ofthe magnetic field causes the muon and electron spins to become progressivelydecoupled from the hyperfine field. The muon polarization can be fully recoveredat high enough fields, above the relevant contact hyperfine field, B0 = Am/ge. Thefunctional form of this LF recovery of the muon polarization is expressed by thedimensionless field variable X = B/B0, and has the well-known form

P ¼ 1=2þ X2

1þ X2(20)

The error in the muon hfccs determined by this technique is typically very large,so this is only used when signals are not observed in TF-mSR or no D1 resonancesare observed in the ALC-mSR spectrum. In muoniated radicals where there issignificant hyperfine coupling with nuclear spins the initial polarization can bebelow 50%. This is because of the presence of nuclear moments and theredistribution of muon polarization among a number of eigenstates at thesefields. In systems where muoniated radicals are slowly formed compared with the


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hyperfine period (1/Am), though still on a fast (Bns) time scale, the repolarizationcurve has two components with a shape indicative of the product of thepolarizations for the prompt initial (Mu) and final state (radical) species(Fig. 8). See the recent work by Fleming et al. on the Mu adduct of bromine fora detailed discussion of repolarization curves.35

2 Organic radicals

2.1 Hyperfine couplings and the determination of structure and dynamics inalkyl radicals

There have been a large number of studies over the last 30 years of the structureand dynamics of muoniated organic alkyl radicals. The structure of a muoniatedradical can be determined by measuring the muon hfcc and as many nuclearhfccs as possible, which maps out the distribution of the unpaired electron. Thisis compared with hfccs obtained from ab initio calculations on the possibleradical structures. mSR is a valuable tool because it is possible to determine notjust the magnitude of the nuclear hfccs, but their signs as well, relative to the signof the muon hfcc, which is very difficult to achieve using EPR. The magnitude andtemperature dependence of the hfccs also provide information about the configu-ration as well as the conformation of free radicals. Configuration refers to thegeometric properties at a nucleus (i.e., planar or nonplanar) and conformationrefers to the dihedral or torsional angles of a radical. In recent years it is commonpractice to obtain the maximum amount of information about the three-dimensional structure of a radical by comparing the measured hfccs withab initio calculations but it is important to understand the general relationshipsbetween hfccs and the configuration and conformation.

The majority of muoniated radicals to have been studied have the muon in the‘‘b’’ position (i.e. attached to an atom that is next to the radical centre, which is

Fig. 8 Repolarization curves for muonium in water and 2-muoxyprop-2-yl radical ((H3C)2COMu) in a1 M aqueous acetone solution. The initial polarization of Mu in water is less than 50% due to a smallamount of spin density delocalized onto the protons of the solvent cage. In the later case there are twocomponents in the repolarization curve; the low field repolarization of the 2-muoxyprop-2-yl radical andthe high field depolarization of Mu.


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referred to as the a position). The reduced hfcc of a nucleus in the b positionobeys the empirical McConnell relation,36

A0X ¼ LþM cos2 y� ��

rp (21)

where L and M are constants (L B{ M), y is the angle between the C–X bond andthe axis of the singly occupied molecular orbital (SOMO) and rp is the spin densityin the p orbital on the a-carbon. L accounts for the effect of spin polarization and Marises from hyperconjugation (or direct overlap) between the pz-orbital containingthe unpaired electron and the C–X bond. The hfcc is modulated with the dihedralangle between the pz-orbital and the C–X bond direction. In the high temperaturelimit, where the system has an energy far above the potential barriers that hinderinternal rotation, all angles y contribute equally to A0X, so that A0X

� �approaches

L + M/2 (assuming that rp = 1). This is one way that the spin density on the a carboncan be determined. As the temperature goes to zero the C–X bond will adopt theminimum energy geometry, and the hfcc will provide information about y. As anexample, if the C–X aligns along the axis of the SOMO (y = 01) then the lowtemperature limit of the hfcc is L + M, whereas if the C–X is aligned at y = 601 thenthe low temperature limit of the hfcc is L + M/4. For a CH3 group, the minima all

have equal energy, so due to symmetry, the value of A0p

D Eis L + M/2, independent

of temperature. The temperature dependence of the hfccs is given by a Boltzmannaverage over ground and excited internal rotational states and the torsionalpotential can be determined from the temperature dependence of the hfccs.

The hfcc of an a-muon or -proton (i.e. one attached directly to the radial centre)also depends on spin density in the p orbital on the a-carbon.36 If the radical centreis planar then the a-nucleus would reside in the nodal plane of the SOMO and as afirst approximation there would be no spin density at the a-nucleus leading to AX = 0.This is not the case due to spin polarization of the C–X bond by the unpairedelectron, which results in negative spin density at the a-nucleus and a negative AX.

A0X ¼ �Qrp (22)

where Q is a proportionality constant that is B70 MHz. The dominant vibrationalmode at the a-carbon is the out-of-plane bend, which moves the substituents out of thenodal plane and into direct overlap with the SOMO, which results in a contribution ofpositive spin density and leads to the magnitude of AX to decrease. If the radical centreis non-planar, which will be the case for all alkyl radicals except the methyl radical,then the hfcc of the a-substituent will depend on the spin density at the radical centreas well as the out-of-plane angle and it will be a delicate balance between spinpolarization and hyperconjugation. The hfccs can change substantially with tempera-ture due to the thermal population of vibrational states and this has been investigatedin great detail using EPR for a range of alkyl radicals with non-planar radical centres,such as the cyclopropyl radical (see for example the work by Barone et al.37,38).

Isotopic substitution has some effects on the vibrationally averaged structure ofa radical. The simplest isotope effect to consider is that on the C–X bond. The ZPEof the C–X (X = Mu, H, D) bond increases as the mass of hydrogen isotopedecreases, and the larger ZPE leads to a longer vibrationally averaged bond lengthdue to the asymmetric bond stretching potential i.e.; hRC–Muin4 hRC–Hin4 hRC–Din.The effect was estimated for C–H and C–Mu fragments using a Morse potential


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with realistic parameters and it was predicted that the vibrationally averaged bondlength in the ground state is longer for C–Mu than for C–H by 4.9%.8 Longer bondstend to result in larger hfccs, either because of better overlap with the singlyoccupied molecular orbital or because of increased spin polarization of the bond bythe unpaired electron. In the muoniated cyclohexadienyl radical A0m is 28% largerthan the methylene proton Ap value.39

Isotopic substitution of a methyl proton destroys the symmetry of the methyl groupby distinguishing one of the particles and Mu substitution has a particularly largeeffect. The torsional potential is the sum of the electronic potential, which isisotopically invariant, and the zero-point energy, which depends on the isotope. Inthe case of CH3 the wells of the torsional potential have the same depth and thebarriers have the same height while the torsional potential of CH2Mu has one well,which corresponds to the C–Mu bond aligned along the SOMO, that is deeper thanthe other two and the barrier heights are no longer equal. This change in the torsionalpotential results in the hfccs changing dramatically as a function of temperature. Aninstructive example is the temperature dependence of the muon and b-proton hfccsin the muoniated tert-butyl radical.40 The muon hfcc decreases with increasingtemperature while the proton hfcc of the protons in the CH2Mu group increase withtemperature (Fig. 9). This shows that the C–Mu bond of the CH2Mu group is alignedalong the axis of the orbital containing the unpaired electron at low temperature.

Fleming and coworkers have measured the muon and proton hfccs of severalmuoniated butyl radicals that were formed by Mu addition to 1-butene and to cis-and trans-2-butene41 and interpreted the results using ab initio calculations.42 Theseradicals are much more complicated systems than the tert-butyl radical due to thelarge number of possible conformers, but surprisingly Fleming et al. demonstrated

Fig. 9 Hyperfine coupling constants of (CH3)2C–CH2Mu in isobutene. The solid lines correspond to fitsfor the liquid solution data and the dotted line to the frozen solution.40


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that the temperature dependence of the muon and proton hfccs could bemodelled assuming a two-fold potential of the form V2(y) = 1

2V2(1 � cos 2y)

together with a Boltzmann weighting of the ab initio calculated hfccs at y = 0and 1201. A somewhat related approach based on ZPE differences from ab initiocalculations was used by McKenzie et al. in studies of Mu adduct of diketene,43 byCormier et al. for the muoniated ethyl radical in CO2 (ref. 44) and by Robski et al.in modelling the Mu adduct of 2-methyl-3-buten-2-ol.45

Lately there has been considerable interest in studying a-muoniated radicals,where the muon is attached directly to the radical centre, as this could providevaluable information about isotope effects on the out-of-plane vibrational modesat the radical centre. Very few a-muoniated radicals have been studied becausethey are difficult to create. Addison-Jones et al. studied the first a-muoniatedradical, the muoniated trimethylsilylmethyl radical ((H3C)3Si–CHMu), which wasproduced by Mu addition to trimethylsilyldiazomethane.46,47 McKenzie et al.showed that a-muoniated radicals can sometimes be formed by the rapiddecomposition of a b-muoniated radical containing a good leaving group likeN2 or CO, which means that a-muoniated radicals can be formed by Mu additionto diazo and ketene functional groups (Fig. 10a). The requirement for theformation of an a-muoniated radical is that the decomposition barrier of theb-muoniated radical must be below the combined energy of the reactants.

McKenzie et al. produced the �CH2Mu and �CD2Mu isotopomers of the methylradical by the reaction of muonium with ketene and d2-ketene, respectively, andmeasured the temperature dependence of the hfccs.48,49 The magnitudes of thehfccs of �CH2Mu and �CD2Mu are larger than those of �CH3 and �CD3 due tolarger zero-point energy in the out-of-plane bending mode. In contrast to �CH3

and �CD3, where the coupling constants become smaller with increasing tem-perature, the negative hfccs of the muoniated radicals were found to increase inmagnitude (i.e. become more negative) with temperature, passing through amaximum near the boiling point of ketene. This behaviour is attributed to asolvent-induced change in the force constant of the out-of-plane bending mode.The opposite temperature effect known for �CH3 and �CD3 is explained byexcitation of the low frequency out-of-plane bending mode. This effect ismuch smaller in the muoniated radicals, where the vibrational frequency issignificantly higher due to the light mass of muonium; consequently, the solventinteraction that modifies the out-of-plane bending frequency dominates at lowtemperatures.

Fig. 10 (a) Formation of an a-muoniated radicals via the decomposition of a b-muoniated radicalintermediate. Suitable functional groups for this reaction are ketenes (X = C, Y = O) and diazo (X = Y = N).(b) Direct formation of an a-muoniated radical. Radicals have been produced from stable singletcarbenes (Z = C), silylenes (Z = Si) and germylenes (Z = Ge).


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A second route to produce a-muoniated radicals is by direct addition of Mu to a lonepair (Fig. 10b). The first example of this was reported by Rhodes et al. who studied theradicals produced by Mu addition to pyridine.50 They found that in addition to theexpected muoniated azacyclohexadienyl radicals there was an additional radical with avery low |Am| (5.8 MHz). It was concluded that this radical formed by Mu addition tothe lone pair of pyridine and that the low muon hfcc is due to the muon residing in thenodal plane of the SOMO and the spin density being delocalized around the six-membered ring. This reaction proceeds because there are low energy empty orbitalsthat can accommodate the unpaired electron, although it is interesting to note that noa-muoniated radical was observed in a 1 M solution of pyrazine in water.51

McKenzie et al. found that a-muoniated radicals could be produced the reactionof Mu with stable singlet carbenes, which are molecules containing a divalentcarbon atom with only six electrons in its valence shell.52 Carbenes are typically veryreactive but recently a number of stable singlet carbenes have been produced; oneis even stable in air! This was the first example of the reaction of a free radical witha carbene and has attracted some attention. The first a-muoniated radicalproduced in this way was by the reaction of Mu with 1,3,4-triphenyl-4,5-dihydro-1H-1,2,4-triazol-5-ylidene, which is a commercially available carbene. The structureof the radical was determined by comparing the experimental Am and AN values withvalues calculated for the three possible structures. Mu added exclusively to thecarbeneic carbon, rather than to the double bond of the triazole ring or the phenylsubstituents. The positive dAm/dT is typically indicative of a non-planar radicalcentre, which was supported by the ab initio calculations, but could also result fromthe increased torsional motion of the phenyl rings, which will result in a decreasein the spin density delocalized around the molecule.

Several a-muoniated radicals have been produced by Mu addition to imidazole-based N-heterocyclic carbenes (NHC)53 and the muon and 14N hfccs have beenmeasured as a function of temperature. Definitive proof that Mu added exclusively tothe carbeneic carbon was obtained by measuring the hfccs of the Mu adduct of1,3-bis-(isopropyl)-4,5-dimethylimidazol-2-ylidene, where the carbeneic carbon was13C-labeled. The resonance due to the 13C was observed and the hfcc matched closelythat calculated for the a-muoniated radical. Several Mu adducts of carbenes have nowbeen studied and the temperature dependence of Am and AN indicates that they havenon-planar radical centres, which is supported by ab initio calculations. The magni-tude and temperature dependence of the muon and 14N hfccs of the a-muoniatedradicals depend greatly on the substituents of the imidazole ring and work is currentlybeing performed to try to explain these effects. DFT calculations indicate that there isno barrier to the reaction at the carbeneic carbon, which accounts for its rapid andexclusive formation even when other unsaturated groups are present.

2.2 Vinyl radicals

The prototypical muoniated vinyl radical, which should be formed by the reactionof Mu with ethyne, has not been observed despite many searches. The vinylradical has been observed by EPR and the coupling constants of the trans and cisb-protons of the vinyl radical are B191 and B95 MHz respectively.54 In themuoniated vinyl radical the a-hydrogen atom flips between either side of thedouble bond, which modulates the spin density at the muon (in the b-position)


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and results in rapid spin relaxation and the TF-mSR lines being broadened beyonddetection.

Several substituted muoniated vinyl radicals have been observed, such asMe3SiCQCH(Mu)55 and Ph–CQCH(Mu).56 The reason that these vinyl radicalshave been observed is that the radical centre is linear, so there is no hoppingbetween configurations and consequently no modulation of spin density at themuon. The Me3Si(Mu)CQCH isomer was not observed for the same reason thatthe muoniated vinyl radical was not observed.

Oganesyan et al. studied the radicals produced by the reaction of Mu with theenediyne compounds (E)- and (Z)-RCRCCHQCHCRCR where R = –CH2CH2CH2CH3

using TF-mSR spectroscopy.57 The assignment of the features in the TF-mSRspectra was aided significantly by DFT calculations. It appears that for bothisomers two vinyl radicals produced by Mu addition to the triple bonds as well asan alkyl radical formed by Mu addition to the double bond. The observation ofboth alkyl and vinyl radicals shows that the rate of Mu addition to double andtriple bonds is of the same order of magnitude but the radical signals did notchange significantly with temperature, so the stated goal of the study, namely tostudy the cyclization reactions, was not possible.

Recently McKenzie has studied the spin relaxation of a substituted muoniatedvinyl radical in zero-field.24 The origin of this experiment was a theory developedby Fedin et al. concerning the spin relaxation rate of radicals with either one ortwo equivalent I = 1/2 nuclei in solution in zero, low and high magnetic fields fordifferent relaxation mechanisms.58 McKenzie determined that a muoniatedradical with no other nuclei with spin could be produced by Mu addition to the1,2-dicarboxyacetylene dianion in aqueous solution. The non-muoniated iso-topomer had been originally studied by Fessenden et al.59 The identity of thisradical was confirmed by measuring the muon hfcc using high TF-mSR andobserving the Mu-like precession in a transverse field of 2 G. The time depen-dence of the muon spin polarization in zero field was best modelled by a singleexponential in accordance with Fedin’s model and the relaxation rate was foundto increase linearly with Z/T, where Z is the viscosity, which indicates that thedominant relaxation mechanism is the modulation of the anisotropic hyperfineinteraction due to molecular rotation. The effective radius of the radical insolution, 1.12 � 0.04 nm, was determined from the relation between lm and Z/T.

2.3 Acyl radicals

Not all b-muoniated radical containing N2 or CO next to the radical centre forma-muoniated radicals. McKenzie et al. studied the reaction of Mu with tert-butylisocynate with the goal of producing a muoniated aminyl radical52 butinstead produced the muoniated N-tert-butylcarbamoyl radical, an acyl radical(Fig. 11).60 McKenzie et al. studied this system with the aid of DFT calculationsand calculated the Mu addition barrier and the barrier for the b-muoniated

Fig. 11 Formation of acyl (Y = O) and thioacyl (Y = S) radicals by the reaction of Mu with isocyantaesand isothiocyanates, respectively. These radicals do not decompose to form a-muoniated radicals.


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radical to decompose. The large zero-point energy in the N–Mu bond results inthe dissociation barrier of the muoniated N-tert-butylcarbamoyl radical beingabove the combined energy of the reactants, in contrast to the N-tert-butylcarbamoyl radical where the dissociation barrier lies below the combinedenergy of the reactants and decomposition is rapid. Nitrogen-centred radicalscould possibly be formed by Mu addition to the azide functional group.

2.4 Mu adducts of aromatic and polyaromatic hydrocarbons

McKenzie et al. studied the radicals produced by Mu addition to p-xylene, anunstrained para-substituted aromatic molecule, and [2.2]paracyclophane, a strainedpara-substituted aromatic molecule, using ALC-mSR.61 The barriers to Mu additionat the different sites of isolated molecules were determined from DFT calculations.Mu addition to p-xylene was significantly preferred at the secondary carbons overthe tertiary carbons. The barriers for Mu addition to [2.2]paracyclophane are lowerthan the barriers for Mu addition to p-xylene, except for addition to the ‘‘endo’’position, where the unfavourable steric interactions with the second ring of[2.2]paracyclophane raises the addition barrier considerably. The lower additionbarriers in [2.2]paracyclophane are due to the release in strain upon formation ofthe radical. Mu was observed to add to both the secondary and tertiary carbons ofp-xylene, with the relative yield of the Mu adduct of the tertiary carbons estimated tobe B10% in the liquid phase and significantly higher in the solid state, althoughthe exact amount could not be determined due to strongly overlapping resonances.The measured relative yields of the three types of Mu adduct of [2.2]paracyclophanedo not reflect the distribution of products calculated using the activation energiesobtained from the DFT calculations due to strong steric interactions with neigh-bouring molecules, which are of the same order as the strain.

There have been several studies of the Mu adducts of polyaromatic hydro-carbons (PAHs). The Percival group has studied two subunits of C70 (pyrene62 andfluoranthene63) as well as triphenylene and dodecahydrotriphenylene. In pyrene,fluoranthene and triphenylene Mu was observed to add only to the secondarycarbons at the edges of the molecules. No addition was observed at any of thetertiary carbons, which is perhaps unsurprising as the resulting radicals mustdistort significantly in order to have a carbon with approximately tetrahedralgeometry. Only in dodecahydrotriphenylene was addition observed at the tertiarycarbons, but this is because there are no unsaturated secondary carbons.

3 Main group and organometallic radicals

3.1 Group 14 containing radicals

An active area of research is the study of the reaction of Mu with Group 14containing molecules and the determination of the structure of the resultingradicals. The Percival–West collaboration have studied the radicals produced bythe reaction of Mu with silylenes and germylenes, which are heavier analogs ofcarbenes.64,65 The high reactivity of these species makes them generally difficultto study and nothing was known about the reactions with free radicals.

It was expected that a-muoniated radicals would be produced by the reactionwith the silylene moiety but the initial experiments were very surprising in that


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the Am values of the Mu adducts of silylenes were much smaller than the expected valuesbased on DFT calculations. The measured Am for the radical produced by Mu additionto N,N0-di-tert-butyl-1,3-diaza-2-sila-2-ylidene was 154.87 � 0.08 MHz while the calcu-lated Am for the a-muoniated radical at the UB3LYP/cc-pVDZ//UB3LYP/6-31G(d) levelwas 764 MHz. This was surprising considering that there was good agreement forthe Mu adducts of carbenes. McCollum et al. elegantly demonstrated that aninitial silicon-centred a-muoniated radical was formed and that this reacts rapidlywith another silylene to give a secondary b-muoniated. This was done byobtaining TF-mSR spectra of a mixtures of two silylenes and observing that fourtypes of radicals were formed by the coupling reaction (Fig. 12). This is the firstdetection of a secondary muoniated radical. The second-order rate constant forreaction of the muoniated silyl radical with the parent silylene was determined tobe 5.7 � 108 M�1 s�1 from the amplitude of the n12 radical signal in the TF-mSRspectra.66 Four types of muoniated radical were produced by the reaction of Muwith a saturated silylene with 3,3-dimethyl substituents.65 The disilanyl radicalthat would be formed by the coupling reaction depicted should exist as a pair ofstereoisomers, which could account for two of the radical signals, but the origin ofthe other two signals is not known. West and Percival suggest that the silylene andmuoniated silylene react to produce conformationally locked dimeric structureswhose interconversion is too slow to be observed on the microsecond time scalebut more experiments need to be performed to confirm this.

Direct evidence for a silicon-centred a-muoniated radical was obtained bystudying a silylene with sterically hindering groups on the nitrogen atoms toprevent dimerization.67 Silylenes with tert-amyl and tert-octyl groups on nitrogen

Fig. 12 (a) Formation of the four types of muoniated disilanyl radicals via the coupling reactionbetween a silyl radical and a silylene and (b) the TF-mSR spectrum of an equimolar mixture of N,N0-di-tert-butyl-1,3-diaza-2-silacyclopent-4-en-2-ylidene (1) and N,N0-di-tert-butyl-1,3-diaza-2-sila-2-ylidene (2) at298 K showing that four types of muoniated radical are formed.64


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dimerized but the signal amplitude decreased due to the larger substituent groupson the silylenes slowing down the coupling reaction. The radical produced by Muaddition to a silylene with 2,6-diisopropylphenyl substituents has Am = 931 MHz, whichis consistent with the a-muoniated radical with the Si–Mu bond oriented almostperpendicular to the ring.

The reaction of Mu with the silylene 3 produced another silicon-centreda-muoniated radical with a large Am (715.74 � 0.05 MHz at 296 K) along with analkyl radical with a smaller Am (148.77 � 0.02 MHz at 296 K) that was formed by Muaddition to the terminal carbon of a butadiene group (Fig. 13).68 The assignmentwas confirmed by the measurement of 14N hfccs and their agreement with valuesobtained from ab initio calculations. Percival et al. also studied the silylene 3 in acomplex with an NHC (4) to see if the NHC complexation protects the Si atom fromattack by Mu. An alkyl radical formed by Mu addition to the terminal carbon of abutadiene group was observed along with a second type of radical with a very smallmuon hfcc (19.0 MHz at 298 K). The second type of radical was concluded to beformed by Mu addition to the silicon atom but with the majority of the unpairedspin density localized on the imidazole ring of the NHC based on the results of DFTcalculations. Unfortunately the small Am for this radical means that any ALCresonances should have negligible intensity, which means that it is not possibleto confirm the structure from the determination of other hfccs.

Another set of silylenes to have been studied have chlorines directly bonded to thesilicon atom.69 One type of muoniated radical was formed by the reaction of Muwith monochlorosilylene 5 with Am being 30.18 � 0.01 MHz at 298 K and increaseswith increasing temperature. Several low-field ALC resonances were observed due tonitrogen and chlorine atoms. The measured hfccs did not match values calculatedfor individual structures and it was assumed that there was rapid interconversionbetween structures 6a and 6b, which differ in the spatial orientation of the Si–Clbond (Fig. 14). The Boltzmann-weighted average hfccs were consistent with theexperimental values. This appears to be the first case where Mu addition does notoccur at the silylene centre. Muon irradiation of the NHC-stabilised dichlorosilylene7 resulted in a muoniated radical with |Am| = 22.04 � 0.01 MHz at 298 K anddecreasing with increasing temperature. The analysis of the ALC-mSR spectraindicated Am to be negative with significant spin density on the chlorine andnitrogen atoms, consistent with structure 8. The temperature dependence of bothCl and Mu hfccs is consistent with a low-temperature conformation in which theSi–Mu bond is close to the nodal plane of the SOMO.

Fig. 13 Muoniated radicals formed by Mu addition to silylene 3 and the silylene-carbene complex 4.68


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Percival and West have also studied the reaction of Mu with germylenes.64 Themuon hfcc of the radical produced by Mu addition to 1,3-di-tert-butyl-1,3,2-diazagermol-2-ylidene is 650.18 � 0.06 MHz, which is consistent with a germanium-centred a-muoniated radical in which the germanium atom has a roughly tetrahedralconfiguration. The measured Am is approximately 20% larger than the calculatedvalue but this is reasonable given the neglect of vibrational averaging in theab initio calculations. There was no evidence for Mu addition to the double bond.Mu was also found to add to the germylene moiety of the closely-related saturatedgermylene, although in this case the measured Am (400 MHz) is substantiallysmaller than the calculated value (839 MHz).

Percival and West have also studied muoniated radicals produced by Mu additionto silene (SiQC) bonds. The first silene to be studied, 1,2,5,5-tetrakis(trimethylsilyl)-silacyclopentene (9), was produced by Kira et al. from the thermal decomposition ofthe silylene 2,2,5,5-tetrakis(trimethylsilyl) silacyclopentane-1,1-diyl.70 Mu wasobserved to add to both sides of the SiQC bond, with the Mu adduct of the Sihaving Am = 186.66 � 0.13 MHz and the C adduct having Am = 136.99 � 0.05 MHz(Fig. 15). The assignment was greatly assisted by the observation of two proton D0

resonances due to the Si adduct. The relative yield of the C adduct was found to bemore than twice as much as the Si adduct, which is in agreement with the predictedheats of reaction. Another system that has been studied is an adamantylidene-silene 12, which was synthesized Apeloig and coworkers. This silene differs from

Fig. 14 Muoniated radicals formed by Mu addition to monochlorosilylene 5 and NHC-stabiliseddichlorosilylene 7.69

Fig. 15 Muoniated radicals formed by Mu addition to the Kira silene 9 and the Apeloig silene 12.65,70


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the Kira silene in that only one type of radical was observed to form, with the measuredAm value being in good agreement with the value calculated for the C adduct.65 Furtherwork is needed to determine what factors affect the reactivity of the SiQC bond.

The Jayasooriya group has used LF-mSR to study the dynamics of the phenylsubstituents in a series of Group 14 tetra phenyl compounds. Jayasooriya et al. madeLF-mSR measurements on Pb(C6H5)4,71 while Stride et al. studied Sn(C6H5)4 andGe(C6H5)4 and Aston et al. studied Si(C6H5)4 and C(C6H5)4. The LF-mSR spectra of allthese compounds consisted of a single relaxing component with a non-relaxingbackground. The longitudinal muon spin relaxation, lm, rate goes through a maximumvalue as a function of temperature for Pb(C6H5)4, Sn(C6H5)4 and Ge(C6H5)4, with themaximum decreasing with temperature for the heavier elements. Stride andco-workers surmised that there is a maximum in lm for Si(C6H5)4 and C(C6H5)4 butthat this occurs at higher temperatures than were accessible experimentally. Themaximum in lm is analogous to the T1 minimum in NMR and occurs when thereorientation rate matches the dominant transition between the radicals hyperfinestates. Inferred values of the reorientation rate show Arrhenius-like behaviour and theactivation energies decrease as the size of the central metal atom increases.

3.2 Group 16 containing radicals

It has been recently shown that muoniated radicals can form in the Group 16semiconductors sulphur and selenium and this work has been extensively reviewedby Cox.6 The interest in sulphur started in the 1950’s when studies suggested that themuons in sulphur were either nearly or completely depolarized. Cox and Reidreported the observation of a D1 resonance at 0.85 T that would correspond to aradical with |Aiso

m | = 233 � 5 MHz.72,73 Webster proposed that Mu reacted with the S8

rings to give a S7 diradical and �SMu,74 which has a 2P electronic structure, based onthe calculated muon hfcc (�184 MHz73 or�171 MHz75). It turns out that the originalALC-mSR spectrum of sulphur appears to be ‘‘the tip of the iceberg’’ and it was actuallythe peak of a much larger feature, which were revealed by measurements on the HiFispectrometer.76,77 At low temperatures there is an initial rapid repolarization at lowfields (up to about 0.1 T) and subsequent broad dip, with a sharp cusp near 0.85 T.Modelling of the ALC spectra indicates that the muoniated radical has Aiso

m =�165 MHz and a large axially symmetric dipolar term of D>

m B �67 MHz. This isconsistent with ZF-mSR spectra up to 100 K where there are precession frequencies at73 and 160 MHz, which indicates that Aiso

m = �184 MHz and D>m = �48.5 MHz. Above

about 100 K, the muon level-crossing resonance shifts to lower field, approaching zerofield at or near the melting point. The shift is accompanied by increasingly fast spinrelaxation, which indicates that the hyperfine parameters are fluctuating withincreasing amplitude at higher temperatures and the time averaged values falling.The assignment of the ALC-mSR spectra is based on supercell density-functionalcalculations. It seems that Mu inserts into a S–S bond of the S8 ring to give a novelbond-centred species S8MuBC. The original bond is elongated by some 55%, but thering structure is not broken. As the temperature increases the ring breaks open andcloses at the site of Mu addition with increasing frequency. The opening of the ringchain-like polyatomic radical �S–S7–Mu, with the muon and unpaired electron locatedat opposite ends of the molecule and this effectively switches off the hyperfinecoupling. The intermittent closing of the ring will result in an intermittent hyperfineinteraction and this provides the necessary mechanism for muon spin relaxation.


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Reid et al. carried out TF-mSR and ALC-mSR experiments on selenium powder.78

There is a very strong D1 resonance that shifts from around 0.8 T at 175 K to 0.865 Tat 50 K, falling again at lower temperatures. These positions correspond to hyperfinecouplings varying between of 216 and 234 MHz, respectively. The n12 and n43 radicalprecession frequencies were observed in polycrystalline Se at 77 and 161 MHz,respectively, which corresponds to Am = 238 MHz. The radical signals in both TF-mSRand ALC-mSR are broadened beyond detection above 200 K. Cox suggests that thebond-centre model should describe the ground state of monatomic H or Mu in Se,although the dynamics will be somewhat different from that of sulphur.6

The prospect of producing the diatomic 2P radicals �OMu, �SMu and �SeMu isremote due to the very rapid spin relaxation that results from the degenerateelectronic ground state. The most likely scenario is that they are observed asquenched species in a solid where the interaction with neighbouring atoms ormolecules breaks the cylindrical symmetry. Another difficulty is producing thesea-muoniated species. It is likely that �OMu could be produced by the reaction ofMu with N2O and �SMu could be produced by the reaction of Mu with OCS.

3.3 Radicals containing transition metals

Organometallic compounds often have 18 valence electrons (VE) as this configura-tion provides enhanced stability, but there are now numerous examples ofcompounds with an odd number of VE, particularly 17 or 19. Short-lived odd-electron molecules could be produced by the addition of a hydrogen (H) atom to adiamagnetic compound with 18 VE. If H adds to the metal atom it will produce a19 VE complex, while if H adds to an unsaturated ligand it will produce a 17 VEcomplex. In addition, by identifying the radicals that form we learn about how freeradicals react with organometallic compounds, which is still an open question.Ferrocene can be considered the prototypical sandwich compound, where there aretwo cyclopentadienyl (Cp) rings are bound on opposite sides of the central ironatom. There are three possible types of radical that could form and their structuresare shown in Fig. 16. Ab initio studies by Macrae indicate that addition to the Cprings is favoured over addition to the iron atom by B80 kJ mol�1.79 The A0m valuesof the exo and endo Cp adducts with a staggered (minimum energy) geometry weredetermined to be 6.5 and �0.9 MHz, respectively, at the B3LYP/6-311+G(d,p) levelwhile the muon hfcc of the Fe adduct is considerably larger with A0m ¼ �95:6 MHz.

Jayasooriya et al. initially studied ferrocene using LF-mSR and the resultingrepolarization curve (initial asymmetry due to paramagnetic muoniated speciesversus applied magnetic field) suggested the formation of a radical with AmB 560 MHz(although this method is notoriously imprecise).80 Jayasooriya et al. observed amaximum in the relaxation rate as a function of temperature (analogous to T1 minimain NMR) from which they determined the correlation time, tc, at each temperatureusing the method of Cox and Sivia.33 Analysis of the temperature dependence of tc

indicated the activation energy of the motion responsible for the spin relaxation to be5.4 � 0.5 kJ mol�1. Jayasooriya et al. also performed ALC-mSR measurements onferrocene and claimed that there were resonances at 1.17, 1.19, 2.04, 2.44 and 3.26 Tfor the low-temperature phase at 18 K due to addition of Mu to both the Fe atom andthe Cp rings.81 The ALC-mSR spectra reported by Jayasooriya et al. are unusual andvery indistinct, especially given that they are displayed in the log(field) format.


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Jayasooriya et al. incorrectly counted the electrons of the Cp adduct, which has 17 VEand not the 19 VE they used for their model. It is likely that the ALC spectra reportedby Jayasooriya et al. are artefacts and further work is needed on this system.

Kubo has determined the diamagnetic muon yields for muons implanted in a seriesof compounds containing acetylacetonate (acac), a common bidentate ligand. PD wasfound to be B1 for paramagnetic compounds like Fe(acac)3 and Nd(acac)3�3H2O andB0.2 for diamagnetic compounds like Al(acac)3, Zn(acac)2�H2O, Ga(acac)3 andLa(acac)3�3H2O.82 The missing fraction in the diamagnetic compounds suggeststhat muoniated radicals are being formed by addition to the central carbon of theacac ligands while in the paramagnetic compounds the reaction of Mu generatesa diamagnetic product. ALC-mSR experiments need to be performed to determinewhether muoniated radicals are formed in the diamagnetic acac compounds butthis appears to be a promising route to generate odd-electron muoniated organo-metallic species. Kubo studied mixtures of diamagnetic acac compounds (Al(acac)3

and Ga(acac)3) and a paramagnetic acac compound (Co(acac)3) and that PD did notincrease linearly with the concentration of Co(acac)3 and suggests that reaction ofMu with Co(acac)3 is faster than the reaction with the diamagnetic compounds.83

4 Muoniated spin probes in soft matter

The structure and dynamics of a number of muoniated radicals, particularly alkyland cyclohexadienyl radicals, are very well understood and these radicals are nowused as probes in more complex systems. Spin labelling with stable free radicalsis a well established technique. It is advantageous to have the probe stand outdramatically from the background, which is certainly the case for radicals in a seaof diamagnetic molecules. The benefit of using muoniated radicals is that they

Fig. 16 (a) Structures of the three possible types of radical that could form by Mu addition to ferrocene(b) ALC-mSR spectra of ferrocene between 18 and 295 K.81


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are formed in situ and have structures that are very similar to their diamagneticparents. Moreover, the hfccs of muoniated radicals are sensitive to the localenvironment, so measuring the hfccs can provide information about the locationof a muoniated spin probe in a system containing hydrophobic and hydrophilicregions. The spin probes also provide information about the local viscosity.In highly viscous environments where the reorientation rate is comparable to theinverse of the muon dipolar hfcc a D1 resonance is observed. The shape of the D1

resonance provides information about the type of motion the probe is undergoing.

4.1 Calamitic liquid crystals

The first mSR experiments on calamitic or rod-like liquid crystals (LCs) wereperformed by the Blundell group on 4-n-pentyl-40-cyanobiphenyl (5CB).84,85 Thiswork has been expanded upon by McKenzie et al. who have used ALC-mSR to studythe molecular dynamics of a series of rod-like LCs; the cyanobiphenyl-based LCs5CB (Fig. 17)86 and 4-n-octyl-40-cyanobiphenyl (8CB),87 4-(trans-4-pentylcyclohexyl)-benzonitrile (PCH5),88 N-(4-methoxybenzylidene)-40-n-butylaniline (MBBA) andcholesteryl nonanoate (CN).89 These molecules rotate rapidly about their longaxis, which generates an axially symmetric hyperfine tensor and they are alignedin the nematic (N) phase and other mesophases by the applied magnetic field. NoD1 resonances were observed in the N phase of 5CB and 8CB, even though themolecule is not undergoing isotropic reorientation, because the angle betweenthe main component of the static hyperfine tensor and the principal rotation axis(aligned along the magnetic field) is approximately 601, so rotation greatlyreduces D>

m , in what can loosely be called an intramolecular version of magicangle spinning. The non-zero D>

m results in shifts of two of the D0 resonances andfrom these shifts it is possible to determine the amplitude of fluctuations of themolecule about its mean orientation. In 5CB and 8CB the mean-squaredfluctuation amplitude increases dramatically as the temperature is increasedtowards the nematic-isotropic phase transition and near the phase transition thelocal environment of the spin probe is like an isotropic liquid, even though thereis macroscopic ordering.

Fig. 17 (a) Structures of the four substituted muoniated cyclohexadienyl radicals formed by the additionof muonium to 5CB (b) ALC-mSR spectra of the Mu adducts of 5CB in the isotropic phase (330 K) and thenematic phase (306 and 280 K). The solid lines represent the best fits to the data and the numbers at thetop of the figure refer to the structures. (c) Temperature dependence of the hyperfine coupling constantshift, DAp, for two of the Mu adducts of 5CB in the nematic phase: Mu-2-5CB and Mu-3-5CB.86


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CN is a rod-like LC that is a derivative of cholesterol and possesses 8 chiralcentres and exhibits a chiral nematic (N*) phase, where there is nematic orderingbut the preferred direction rotates throughout the sample, between 364.3 and348.2 K and a Smectic A (SmA) phase, where the molecules form well-defined layerswith the molecular axes oriented along the layer normal, below 348.2 K. Thechemical structure of CN is fairly complicated but the presence on a single doublebond makes it a very simple system for muon labelling.89 Mu adds to secondarycarbon of the double bond. Two stereoisomers are produced but only one (with Muin the b position) is observed as the second stereoisomer has almost no spindensity at the muon. A D1 resonance was observed in the mesophases of CNbecause the angle between the main component of the static hyperfine tensor andthe principal rotation axis does not result in effective averaging of the hyperfinetensor and results in a larger D>

m value. In the N* phase of CN the D1 and D0

resonances narrow with increasing temperature due to the increased amplitude ofthe fluctuations about the director decreasing the magnitude of D>

m , which is givenby 2/3fwhm(D1)gm. The mean-squared fluctuation amplitude of the spin probe wasfound to increase linearly with temperature. The D1 resonance is still present in theisotropic phase and broadens with increasing temperature due to the slow isotropicreorientation of the spin probe. The reorientation rates were determined from acomparison of the width of the D1 resonance with simulations using ‘‘Quantum’’.30

4.2 Discotic liquid crystals

ALC-mSR has been used to study two closely related discotic LCs; 2,3,6,7,10,11-hexahexyloxytriphenylene (HAT6)90 and 2,3,6,7,10,11-hexahexylthiotriphenylene(HHTT).91 The ALC-mSR spectra of the discotic LCs are very different from those ofthe calamitic LCs because of the interaction between the p-system of themuoniated radical and those of neighbouring molecules. In both HAT6 andHHTT Mu adds to the unsaturated secondary carbons of the triphenylene ring. InHAT6 there are two small and narrow resonances that are superimposed uponvery broad and intense resonances that appear to be independent of temperature.The small resonances are the D1 and methylene proton D0 resonances of highlymobile muoniated radicals that are trapped between the columns of HAT6molecules. The D1 resonance of these radicals disappears at the transition fromthe hexagonal columnar (Colh) mesophase to the isotopic phase. The very broadand intense resonance in both the Colh and I phases is believed to result frommuoniated radicals within the HAT6 columns. In HHTT there are no narrowresonances due to radicals between the columns. There is a single very broad andintense resonance in the Colh and I phases that is much larger than the multipleresonances in the crystalline (Cr) and helical (H) phases and it changes substan-tially with temperature (Fig. 18). The large resonance is due to Mu adducts ofHHTT that are incorporated within the stacks of HHTT molecules as isolatedparamagnetic defects. The resonance lineshape in the Colh and I phases is due toextremely rapid electron spin relaxation that is on the order of a hundred-foldfaster than in the H or Cr phases. The electron spin relaxation rate increasessignificantly with increasing temperature and appears to be caused by the liquid-like motion within the columns, which modulates the overlap between thep-system of the radical and the p-systems of the neighbouring HHTT molecules,and hence, the hyperfine coupling constants.


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4.3 Lyotropic systems and the partitioning of co-surfactants

Surfactants are molecules with functional groups that have widely differing affinitiesfor water and that can self- assemble in aqueous solution to form a number ofremarkable structures including ‘‘lamellar’’ liquid crystalline phases where thesurfactant molecules form arrays of regularly separated bilayer ‘‘sheets’’ separatedby solvent. Subtle changes in the microstructure of the bilayer can have dramaticeffects on macroscopic behaviour, which can be brought about by changes insurfactant and electrolyte concentrations or by the addition of a cosurfactant. Thecosurfactant may have additional roles, such as being a fragrance or a dye. They aretypically present only in very low concentrations, which makes them difficult tostudy using traditional spectroscopic techniques as the signals from these mole-cules are swamped by signals from the more numerous solvent molecules.

ALC-mSR is an excellent tool for studying cosurfactant molecules with aromaticfunctional groups because it is sensitive only to the muoniated radicals thatare formed from Mu addition to the cosurfactant and not to the diamagnetic

Fig. 18 (a) The optimized structure (UB3LYP/6-311G(d,p)) and distribution of unpaired electron spindensity (PBE0 with EPR-II for C and H and 6-311G(d,p) for S) of the Mu adduct of HHTT. Grey atom =carbon, light grey (online version: yellow) atom = sulphur, white atom = hydrogen/muonium. Positivespin density is dark grey (online version: blue) and negative spin density is light grey (online version:green) (isovalue = 0.004). Calculated Am and Ap values greater than |5| MHz are reported along with theD1 and D0 resonance fields. The dipolar hyperfine coupling constants (Bm and Bp) are reported for themuon and methylene proton. (b) Background-subtracted ALC-mSR spectra of HHTT as a function oftemperature in the Cr, H, Colh and I phases.91 The spectrum at 302 K is the uppermost and narrowestcurve and the spectrum at 377 K is the lowermost and broadest curve.


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non-muoniated molecules. The cosurfactant traps most of the muons, eventhough it is present in very low concentrations, because Mu reacts much morerapidly with the phenyl ring (kM = (1.9 � 0.4) � 109 M�1 s�1) than with thecarbonyl (kM o 108 M�1 s�1) or other unsaturated bonds in the surfactant.ALC-mSR can be used to study cosurfactants containing phenyl groups withconcentrations as low as 1 mM.

4.3.1 Solvent effects on hyperfine coupling constants. The hfccs provideinformation about the local environment, as they are sensitive to interactionsof the radical with the neighbouring molecules. The shifts in the position of D0

resonances due to solvent interactions are small but they can be measuredvery accurately. The methylene proton hfccs of the muoniated cyclohexadienylradical,92 the three Mu adducts of 2-phenylethan-1-ol (PEA)93 and the three Muadducts of 5-phenylpentan-1-ol (PPA)94 have been measured in a variety ofsolvents and were observed to shift in a systematic way with the polarity of thesolvent (Fig. 19). The ‘‘% aqueous character’’ of the radical in a solvent ‘X’ wasdefined in terms on the relative position of the D0 resonance in the solventcompared with the positions of the D0 resonances in H2O and C18H38.

%aq: char: ¼ BXres � BC18H38

res

BH2Ores � B

C18H38res

(23)

Vujosevic et al. found that the position of the methylene proton D0 of theC6H6Mu radical depends approximately linearly on the concentration of hydroxylgroups and developed a model based on that of Reddoch and Konishi95 thatexplains this observation.92 The basis of the model is the recursive relationbetween the dipole moment of the C6H6Mu radical, which partially aligns thedipole moments of the surrounding solvent molecules, and the electric fieldgenerated along the dipole moment of C6H6Mu radical by the solvent, whichalters the electron distribution in the radical and hence, the dipole moment andthe hfccs. This is in agreement with the ab initio calculations of Straka et al. usingthe polarized continuum model and explicit water molecules.96 The solventmodel described above can even explain Am values in exotic solvents like ionicliquids.97,98

Fig. 19 (a) Structures of the three possible Mu adducts of 2-phenylethan-1-ol (PEA). No Mu addition isobserved at the unsaturated tertiary carbon. (b) D0 resonances of the three isomers of the muoniatedcyclohexadienyl radical in a dilute solution of PEA in n-octadecane (top), bulk liquid PEA (middle), and ina dilute solution of PEA in water (bottom) at 308 K. (c) Polarity diagram for 40 mM PEA in varioussolvents, obtained from the relative resonance positions of PEA-Mu compared to H2O and C18H38.93,100


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An interesting observation was that there is a considerable difference between themethylene proton hfccs in benzene and octadecane, even though both solvents arenonpolar. The difference arises from the interaction of the C6H6Mu radical’s dipolemoment with the quadrupole moment of the surrounding benzene molecules andDilger et al. predicted that the methylene proton hfcc should be directly proportionalto the concentration of solvent quadrupole moments.99 The predictions of thismodel were verified experimentally in mixtures of benzene and cyclohexane.

The % aqueous character of the ortho and meta isomers of the Mu adduct ofPEA were shown to depend linearly on the dielectric constant, with the notableexception of ethyl acetate. Another inconsistency is the % aqueous character ofthe para isomer, which is consistently low for methanol and less polar solvents.The reason for this discrepancy has not been determined but it has beenspeculated that the radical adopts a geometry in the non-polar solvents withthe hydroxyl group strongly interacting with the cyclohexyl moiety.

4.3.2 ALC-lSR of muoniated radicals in bilayers. ALC-mSR has been used tostudy the partitioning of phenyl alcohol cosurfactants in bilayers of the dichaincationic surfactants 2,3-diheptadecyl ester ethoxypropyl-1,1,1-trimethylammoniumchloride (DHTAC) and diocta-decyldimethylammonium chloride (DODMAC), theanionic surfactant sodium n-dodecyl sulfate (SDS), and the nonionic surfactanttetra(ethylene glycol) n-dodecyl ether (C12E4).93,100–103 Several phenyl alcoholcosurfactants were studied with different lengths of alkyl chain; 2-phenylethan-1-ol(PEA), 3-phenylpropan-1-ol, 4-phenylbutan-1-ol, 5-phenylpentan-1-ol (PPA), andp-propyl-2-phenylethan-1-ol.

DHTAC forms bilayers that undergo a structural change between 328 and 330 K(determined by SAXS); below this temperature, the system is in the Lb phasewhere the motion of the alkyl chains is limited, and above this temperature, it isin the La phase and the alkyl chains have considerable mobility. The ALC-mSRspectrum of PEA in DHTAC in the low temperature Lb phase has three D0

methylene proton resonances but no D1 resonances, indicating that the motionof the radical is isotropic (Fig. 20).93,100 The position of the D0 resonances indicate

Fig. 20 (a) ALC-mSR resonance spectra of PEA in DHTAC at various temperatures. (b) Local polaritydetermined from the D0 resonance positions as a function of temperature. (c) Schematic diagram of theortho isomer of PEA-Mu in the DHTAC bilayer (top) and in the aqueous region (bottom).93


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that the radicals are in an aqueous environment. The PEA-Mu radicals (and byinference the PEA molecules) have difficulty penetrating into the bilayer in the Lb

phase because of the tight packing of the alkyl chains. D1 resonances are present in theLa phase, which indicates that the motion of the radical is anisotropic, likely aroundthe long axis of the molecule, and the D0 resonances have shifted to a lower field,which indicates that the radicals are in a less polar environment. The meta-PEA-Muisomer appears to be in a more non-polar environment than the ortho isomer and thiscould be evidence of a water gradient within the bilayer. The low polarity sensed by thepara isomer is likely overestimated due to the reasons discussed above. Near the La–Lb

transition there is coexistence between radicals in the bilayer and in the aqueousregion. The location of the muoniated radicals was confirmed by studying the reactionbetween the radicals and paramagnetic Ni2+ cations, which do not partition into thebilayer (Fig. 21).104 The spin-exchange rate, kex, was determined from the width of theD0 resonances and the average value of kex for the three isomers was found to be tentimes smaller in the La phase. Increasing the alkyl chain length increases thepenetration of the phenyl ring into the Lb phase, as shown by the progressive shiftof the D0 resonances to lower fields going from PEA to 5-phenylpentan-1-ol.101

ALC-mSR spectra of PEA in DODMAC have D1 resonances in both the La and Lb

phases, which indicates that the PEA-Mu radicals reside within the bilayer, regardlessof the phase. The D1 resonances in DODMAC have a much larger amplitude thanthose in DHTAC, which means that the dipolar coupling is larger in DODMAC andthat the PEA-Mu radicals in DODMAC are more aligned and have less mobility.

4.3.3 Muoniated spin probes in Micelles. Dawin et al. recently used ALC-mSRto resolve a controversy about the role of the chiral dopant in inducing the chiralnematic (N*) phase of a lyotropic liquid crystal (LLC) composed of anisotropic

Fig. 21 ALC-mSR spectra of the Mu adducts of 2-phenylethanol in aqueous NiCl2 solutions. The D0

resonances of the three isomers broaden because of the spin-exchange reaction with paramagnetic Ni2+.104


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amphiphile micelles.105 In one model the N* phase results from dispersive chiralinteraction between dopants at the surfaces of adjacent micelles and in the othermodel the N* phase results from the chiral dopant being located within the micelleand distorting its structure. Dawin et al. studied a series of chiral amphiphileswith the same chiral polar head group but increasing aliphatic segment lengthconnecting a phenyl ring. The position of the D0 resonances in the LLC comparedwith water and decanol strongly indicates that the dopants are located at the micellarsurface and the %aq. char. of the local environment was found to decrease withincreasing chain length, which suggests that the longer chain allows the aromaticring of the dopants to penetrate deeper in the micelle (Fig. 22). (R)-Mandelic acid(R-MA) (n = 0) and (2R)-2-hydroxy-4-phenylbutanoic acid (R-HPBA) (n = 2) havehigh helical twisting power (HTP) and broad D1 resonances are clearly presentin the ALC-mSR spectra, while no D1 resonance is observed in (R)-phenyllactic acid(R-PLA) (n = 1), which has a very low HTP. The results indicate that the ability of thedopant to induce the helical superstructure is related to the dynamics of the dopant.Dawin et al. propose that the chiral polar head groups of R-MA and R-HPBA interactstrongly with the polar headgroups of the surfactant molecules and are effectivelyimmobilized on the timescale of the muon lifetime, while the head group of R-PLAsticks out of the surface and interacts much less with the polar headgroups of thesurfactant molecules, which allows it to rotate more rapidly and reduces both the D1

resonance intensity and the chiral induction.The studies described in this review are just scratching the surface of what is

possible using the mSR technique and there are a wide range of closely relatedsystems of biological importance that could be investigated. Except for themissing phosphate group, the DHTAC surfactant molecules are analogs of thetypical phospholipid molecules which are the main constituents of cell mem-branes of living organisms and the DHTAC bilayers are therefore a simple modelsystem of a cell membrane. Roduner has noted that mSR could be used todetermine whether a drug molecule resides mostly in the aqueous medium of a cellfluid or whether it intercalates into the cell membrane and could therefore be used forstudying some basic drug formulation problems.106 There has been a repolarization

Fig. 22 (a) Linear decrease of the relative polarity (RP) for the para D0-resonance with increasingmethylene chain length n(CH2) of the dopants. (b) Schematic model of the dopant location at themicellar surface. Red: O, grey: C, bright green: H, blue: N or ammonium head group. The Br� counter ionsand the n-octadecane are neglected for simplicity reasons.105


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study of the Mu adducts of cholesterol in liposomes composed of DPPC(dipalmitoylphosphatidylcholine) and this area is ripe for exploitation.107 A word ofcaution is needed as mSR will only be useful in well-defined systems where a limitednumber of types of muoniated radical are formed and these can be characterized byTF-mSR or ALC-mSR.

4.4 Polymers

mSR has been used to study conjugated and non-conjugated polymers. Muoniatedradicals can be introduced as probes in non-conjugated polymers by the reaction ofMu with isolated unsaturated bonds or phenyl groups. The first muoniated radical ina non-conjugated polymer was produced by Jestadt et al.108 They produced localizedalkyl radicals by the reaction of Mu with polybutadiene (PBD) and measured themuon and b-proton hfccs by TF-mSR and ALC-mSR (Fig. 23). The Am value determine byTF-mSR decreases in magnitude with increasing temperature. The radical signals arestrong and narrow at high temperature because of efficient dynamical orientationalaveraging of the hyperfine anisotropy and broaden substantially as the temperature islowered and the polymer dynamics slow down. The D1 and D0 resonances shift tolower magnetic field as the temperature is increased, indicating a decrease in themuon and b-proton hfccs. The temperature dependence of the hfccs could provideinformation about the conformation of the polymer chain but this detailed analysishas not been performed. Similar effects are found for polystyrene (PS), where it is thependant phenyl groups that are labeled rather than the main chain.109

LF-mSR can be used to study various dynamical processes in non-conductingpolymers as motion of the polymer causes modulation of the hyperfine interactiontensor. Pratt et al. measured the longitudinal muon spin relaxation rate in PBD110

and PS109 and found that the glass transition temperature, Tg, could be determinedfrom the temperature dependence of lm. In both PBD and PS lm increases linearlywith temperature above Tg while below Tg lm is approximately independent oftemperature, except for an unexplained step in lm in PS at BTg � 20 K. Pratt et al.have attempted to determine the depth dependence of Tg near the surface of PSusing low-energy muons and claimed to have evidence of a mobile surface regionB35 nm thick.111 This work must be praised for its novel nature but is likelyincorrect due to the relaxation rates being measured in zero magnetic field where

Fig. 23 (a) The structure of the muoniated alkyl radical formed by Mu addition to polybutadiene.(b) The associated correlation spectrum for polybutadiene as a function of temperature. (c) ALC-mSRspectra of polybutadiene.108


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many transitions are allowed. A study by Clayden et al. of polyurethane using LF-mSRdid not provide useful information about molecular dynamics as there was no cleartemperature dependence of lm, mainly due to poor statistics.112

Muoniated radicals can also form in conjugated polymers but the unpaired spin ishighly mobile and can rapidly diffuse away from the muon leaving it in an effectivediamagnetic environment. Every time the unpaired spin returns to the carbonadjacent to the muon, the muon-electron hyperfine coupling is turned on and thenoff, so that successive visits progressively relax the muon polarization. Measurementof the magnetic field dependence of this relaxation yields the spectral density functionassociated with the random walk of the unpaired spin and can be used to infer thedimensionality of the diffusion. NMR or EPR can be used to study the motion ofpolarons in doped conducting polymers but mSR is unique in that it can be used tostudy polaron transport in undoped materials (in which there is no significant carrierdensity to provide an NMR or EPR signal). Another advantage of mSR is that it canprovide information on the intrinsic transport processes governing the mobility of anelectronic excitation along a chain while transport experiments are inevitablydominated by the slowest component of the transport process. The use of the muonas a probe of electron motion in conducting polymers has been reviewed by Pratt.113

The first example of this was the study by Nagamine et al. of the trans isomer ofpolyacetylene (PA).114 In these studies the longitudinal muon spin relaxation wasmeasured and the main source of muon relaxation was attributed to hyperfinecoupling between muons bonded to the polymer and mobile electronic excitationsin the form of solitons which are able to move relatively freely along the polymerchain. At first the data were analyzed using an exponential relaxation function andan expression for the relaxation rate which was originally derived for NMR in ananisotropic system with diffusive spin motion. The longitudinal spin relaxation ratein trans-PA was found to be proportional to B�1/2, which implies a purely one-dimensional diffusion process. In a subsequent analysis of the data the timedependence of the polarization was determined to be non-exponential.115

The results of measurements on the cis-PA are completely different from thetrans isomer. A very small residual asymmetry was measured at low fields withonly very weak relaxation and a repolarization curve was observed, with fullasymmetry was regained for fields above 10 mT. It was proposed that the solitonis trapped at the muon site, due to the absence of degeneracy in the bond-alternation ground state for this isomer. The muon hfcc of the localized state incis-PA was determined to be 91 MHz from TF-mSR and ALC-mSR measurements.116

Fisher et al. studied the muoniated states in trans- and cis-PA using acombination of semi-empirical calculations and classical Newtonian equationsfor motion of the ions.117 They found that the spin density is localized near themuon in cis-PA but that the magnitude of the muon hfcc depends on defectspresent in the polymer chain. The difference in the structure and properties of theextended spin defect for the two isomers on addition of muonium were consistentwith the experiments of Nagamine and coworkers.

Risch and Kehr developed a direct stochastic theory of muon spin relaxation intrans-PA based on the one-dimensional diffusion of defects along the polyacetylenechains.118 The random walk of the unpaired electron along the polyacetylene chainprovides a fluctuating hyperfine interaction with the muon and is the mechanismfor the relaxation of the muon spin. Risch and Kehr noted that the correlation time


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for a particle undergoing one-dimensional diffusion to return to the origindiverges so the standard NMR theory used for the earlier data analysis byNagamine et al. cannot be used. The general form of the muon spin relaxationfunction in the Risch Kehr (RK) model is

PzðtÞ ¼ Pzð0ÞeGterfcffiffiffiffiffiGtp

(24)

for ltmax c 1. l is the electron spin flip rate, tmax is the experimental time scaleand erfc is the complementary error function. The RK model shows the correctnon-exponential relaxation and the t�1/2 behaviour at long times. Fits of the timedependence of the muon spin polarization in trans-PA were quite good at finitefields but poor at zero field.

In finite magnetic fields the relaxation rate parameter, G, is given by

G ¼ l

1þDk

ffiffiffiffiffiffiffiffiffiffi2oelp

o02

� �2 (25)

where oe is the electron Larmor frequency, o0 = 2pAisom is the isotropic hyperfine

coupling constant when the unpaired electron is localized on the neighbouringsite to the muon and DJ is the intrachain diffusion rate. In high magnetic fieldsthe relaxation parameter is proportional to B�1 and independent of the electronspin relaxation rate, with

G ¼ o04

2oeDk2(26)

which allows for a straightforward determination of DJ if one has a reasonableestimate of Aiso

m . The interchain diffusion rate, D>, can be estimated in cases ofrapid diffusion (i.e. eqn (26) is valid at low fields). This is seen as a deviationof G at low magnetic fields from the B�1 dependence.113 The RK model does notinclude interchain diffusion so an empirical low-field cut-off is introduced ofthe form

G = G0/(1 + o/D>) (27)

LF-mSR has been used to measure the microscopic diffusion rates in differentconjugated polymers such as polyaniline,119 polypyridine,110 and polyphenylene-vinylene120 and Risdiana et al. have recently studied electron conduction insubstituted polythiophenes.121–123 The majority of conducting polymers havenon-degenerate ground states that cannot support free solitons but the spindefect can still move away in the form of a negative polaron, which leaves behinda positive charge near the muon site. The LF-mSR experiments have shown thatthere are mobile spins in a wide variety of conducting polymers (Fig. 24).

The work on conducting polymers has great potential but it must be viewedcautiously. The RK model is a powerful tool to determine important parametersabout motion at the molecular level but there is the danger that this RK modelis often applied indiscriminately. Many processes lead to a decrease in thespin relaxation rate with increasing magnetic field. Researchers must verifythat the RK model is appropriate and not use it just because it gives fits withgood w2 values.


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5 Organic semiconductors

Semiconducting organic materials are being considered for use in a vast array ofelectronic applications and there is considerable research in this area in order tobetter understand the behavior at the molecular level. In 2008 Drew et al. claimed tohave measured the intrinsic hopping rate of electrons in the organic semiconductortris[8-hydroxy-quinoline]aluminum (Alq3) using LF-mSR.124 This claim generatedconsiderable interest as it is very difficult to extract intrinsic transport propertiesfrom bulk transport measurements, which are typically dominated by extrinsicproperties such as intergrain hopping, and draws on the strength of the muon as alocal probe. Drew et al. analyzed the LF-mSR spectra using the Risch–Kehr modeland concluded that the electron was hopping at a rate of 1.4 � 0.2 � 1012 s�1 at290 K based on the magnetic field dependence of the RK relaxation rate, G p B�1.

Unfortunately this conclusion appears to be incorrect as Drew et al. did notconsider the local environment of the muon and the differences between theelectronic structure of Alq3 and the Mu adducts of Alq3. Drew et al. implicitlyassumed that the muon was a passive probe and that the unpaired electron fromMu went into the lowest unoccupied molecular orbital (LUMO) of Alq3, in essenceallowing the material to be doped at an incredibly small level. McKenzie used DFTcalculations to show that the electronic structure of the Mu adducts of Alq3 areconsiderably different from that of Alq3.125 The highest occupied molecularorbitals (HOMO) of the Mu adducts of Alq3 lie in the HOMO–LUMO gap ofAlq3. It was shown that electron transfer in either direction between the Muadducts of Alq3 and a neighbouring Alq3 molecule would be very unfavorable andthat the muon effectively ‘‘pins’’ the unpaired electron. McKenzie proposed that

Fig. 24 (a) The structure of polyaniline : emeraldine base (PANI : EB) (b) Magnetic field dependence ofthe RK relaxation parameter observed in PANI : EB at 6 K and at 300 K. (c) The temperature dependenceof the intrachain DJ and interchain D> diffusion rates in PANI : EB.113


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ALC-mSR spectroscopy could be used to confirm whether the electron is localized orextensively delocalized as claimed by Drew et al. The localized electron spin densitywould give rise to D1 and methylene proton D0 resonances between 0.8 and 1.9 T. ALC-mSR measurements on the heavier analog tris[8-hydroxy-quinoline] gallium (Gaq3) haveshown several resonances in this field range (Fig. 25),126 which confirms that theunpaired electron is localized. ALC-mSR experiments on Alq3 are eagerly anticipated.

Schulz et al. have studied several other organic semiconductors including twofunctionalized acenes (polycrystalline tri(isopropyl)silyl-pentacene and amorphous5,6,11,12-tetraphenyltetracene), rubrene and the aforementioned Gaq3.126 There areseveral resonances in the ALC-mSR spectra but these have not been properly assignedto specific radical structures. They observed an increase in the amplitude and widthof the ALC resonances with increasing temperature and concluded that the electronspin relaxation rate was increasing with temperature. This may be true but morework is needed to understand what the mSR results say about the properties of thesematerials as the cause of the relaxation could be intramolecular in origin.

6 Biological materials

In a previous section it was noted that the mSR studies on model membrane couldbe extended to systems of biological importance but only in systems with welldefined radical states. The desire to use mSR to study radicals in complicatedbiological materials containing many different types of molecules and environ-ments is praiseworthy but likely doomed to failure due to limitations with the mSRtechnique. In the studies on model bilayers described above the muon is‘‘directed’’ to a desired location by the suitable choice of target material andexploiting the different rates of addition for Mu with different functional groups.This type of direction is not possible in a biological material like a protein or DNAas there are multiple sites with very similar Mu addition rates, which can lead tothe formation of many types of radicals with a wide range of Am values. As anexample Scheicher et al. used DFT calculations to determine the Am values of thelikely Mu adducts of thymine in A- and B-form DNA and described seven radicalswith the muon hfcc ranging from 47 to 238 MHz.127 The formation of multiple

Fig. 25 (a) Structure of Xq3, where X = Al and Ga. Hydrogen = white, carbon = gray, nitrogen = blue,oxygen = red, and aluminum/gallium = pink. (b) ALC-mSR spectra of Gaq3 at 10 and 300 K.126


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radicals in DNA is supported by a ALC-mSR study of the constituents of DNA byHubbard et al.128 The spectra are of very poor quality but it appears that at leasteleven types of radical were formed with Am between 150 and 657 MHz. Inbiological systems where multiple radicals are formed the muon polarizationwill be spread out among each species, which will result in the signal from eachdifferent type of radical having negligible intensity.

Many researchers have performed LF-mSR measurements on biological materialssuch as proteins, DNA,129–131 even blood,132,133 with the goal of measuring electronhopping rates in these materials in analogy to the studies on conducting polymers.The relaxation rate for each site will depend on the hyperfine parameters of theresulting radical and it is not appropriate to use the RK model as some studies haveand use an ‘‘average’’ Am value, especially when the range of Am values and their relativeweighting is unknown. The resulting ‘‘hop rate’’ is meaningless. Another problem withmany of the LF-mSR experiments is that it is highly likely that the unpaired electron islocalized near the muon, so that the relaxation could be the result of moleculardynamics modulating the isotropic or dipolar hyperfine interactions. The key tosuccess in using mSR to study biological materials is to pick the system carefullyand ensure that there a minimum number of different types of radicals are formed.

Clayden et al. have studied the dynamics of dioleoyl phosphatidylcholine (DOPC)in the solid state using LF-mSR.134 This is an ideal system as the muoniated radicalsthat form via Mu addition to the CQC bonds will have approximately the samehyperfine parameters. There are two maxima in the longitudinal field muon spinrelaxation rate between 100 and 400 K, with the authors proposing that the peak at250 K results from the onset of the muoniated radical being able to undergotorsional or crank-shaft type motions and the peak at 350 K results from largeamplitude motions possible in the less sterically constrained fluid phase. Rhodeset al. studied the dynamics of two dipeptides in the solid state using LF-mSR.135 Inboth glycylglycine and a doubly protected alanylalanine derivative two peaks wereobserved in the longitudinal muon spin relaxation rate as a function of tempera-ture and this was used to determined activation energies for molecular motions ofthe muoniated radicals, although the radicals have not been characterized suffi-ciently to determine the structure and dynamics.

7 Radicals in extreme environments

7.1 Supercritical water

Supercritical water (SCW) has attracted much attention in recent years because ofits unique properties, such as low viscosity, low density, low polarity and the highsolubility of organic compounds and its potential use as a green solvent. Studyingfree radicals in SCW is technically challenging due to the high temperature andpressure of the critical point (647 K, 221 bar). There are no reports of radicals inSCW using EPR and only one report of the observation of the triphenylmethylradical in subcritical water (at 573 K) using EPR.136 SCW is an ideal system tostudy using mSR because the m+ can penetrate a thick-walled vessel required towithstand the high pressures and stop in the fluid sample and the high-energyemitted positrons, which convey the spectroscopic information, can also penetratethe walls and be detected outside the container.137


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Numerous muoniated free radicals have been observed in SCW over the last twelveyears. The first radicals to be observed were the cyclohexadienyl radical and the tert-butyl radical.138 The success of this study was due to a thorough understanding ofsome unusual features of SCW. Benzene is only sparingly soluble in water understandard conditions, so it is impossible to obtain TF-mSR spectra of the C6H6Muradical in aqueous solution at room temperature. Percival et al. were able to obtainTF-mSR spectra of the C6H6Mu radical in SCW because benzene is completely misciblewith water at elevated temperatures and pressures.139 The muon hfcc of the C6H6Muradical decreased approximately linearly with increasing temperature and is largerthan the corresponding value at the same temperature for liquid benzene39 and in thegas phase.140 This is in agreement with the solvation model of Vujosevic et al.92

Another clever trick was used to obtain TF-mSR spectra of the tert-butyl radical;use a water-soluble starting material that coverts to isobutene in SCW. The water-soluble compound, tert-butanol, undergo rapid dehydration to isobutene, whichthen reacts with Mu to form the tert-butyl radical. The assignment of the radicalwas based on the magnitude of Am, which was determined by TF-mSR, and the Ap

values, which were determined by ALC-mSR.141

The Percival group has studied the conversion between the keto and enol formsof acetone in SCW using TF-mSR.142 The equilibrium constant for acetone at roomtemperature is firmly on the side of the keto form, with the enol content beingapproximately 6 � 10�7%. At room temperature, the rate constant for Muaddition to enol form of acetone is B102 times greater than that for additionto the keto form but the relative small abundance of the enol form results in theobservation of only the Mu adduct of the keto form. Below B520 K a single type ofradical with a very small muon hfcc was observed. The magnitude of Am isconsistent with the 2-muoxy-prop-2-yl radical,143 albeit with a small shift that isconsistent with the difference in solvent properties for different concentrations ofacetone. The positive temperature dependence of Am has been interpreted interms of hindered internal rotation about the C–O bond in (CH3)2COMu, with aminimum-energy conformation in which the O–Mu bond is very close to thenodal plane of the p orbital containing the unpaired electron.143,144

The TF-mSR spectrum of this system is considerably different above 520 K inthat the muon hfcc of the observed radical is much larger than that of the2-muoxy-prop-2-yl radical. The muon hfcc of the observed radical is about250 MHz and falls with temperature, which is typical behaviour for a b-muoniatedalkyl radical. The radical was assigned as the 1-Mu-2-hydroxy-2-propyl radical(CH3C(OH)CH2Mu), which is formed by Mu addition to the enol form of acetone.At high temperature, the rate constants for Mu addition to the keto and enoltautomers will be approximately equal, at a limit imposed by collisions in thesolvent cage, and the shifting of the equilibrium constant with temperatureresults in Mu addition to the enol form dominating. Percival et al. concluded thatthe enol concentration in SCW was greater than 0.1 M.

The assignment of the Mu adducts of the keto and enol tautomers was confirmed bydetermining proton hfccs using ALC-mSR.141 A single resonance was observed at 0.137 Tat 365 K, which is due to protons with Ap = 57.9 MHz, and was assigned as resultingfrom the two methyl groups. The ALC-mSR spectrum at 623 K contained two closelyoverlapping resonances near 1 T that were due to protons with Ap of 62.5 and 59.7 MHz.These were assigned to be the protons in the CH3 and CH2Mu groups, respectively.


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7.2 Supercritical carbon dioxide

Supercritical CO2 (scCO2) has been found to be a useful ‘‘green’’ solvent for a widevariety of chemical applications and the supercritical region (Pc = 7.38 MPa and Tc =304.15 K) is technically much easier to generate than SCW. The mSR experiments onscCO2 are unique because CO2 has no hydrogen atoms, so it is not possible toproduce reactive species like H and OH, which are needed to create neutral radicals.The first muoniated radical to be observed in scCO2 was the muoniated ethyl radical(MuH2C–CH2), which was produced by Mu addition to ethene.44 The identity of thisradical was confirmed by measuring the muon and proton hfccs using TF-mSR andALC-mSR, respectively. The magnitude of the hfccs indicates that the MuH2C–CH2

radical does not react with CO2 as has been previously proposed. Am was observed tohave an unusual pressure dependence at 373 K, decreasing with increasing pressure,except around a density of B0.4 g cm�3 where there is a local minimum in Am. Thehfccs are assumed to decrease with increasing density due to an increase in thenumber of collisions between the ethyl radical and surrounding CO2 molecules,which result in a partial transfer of unpaired electron density to CO2, and a decreasein the mean ethyl radical – CO2 distance, which results in a larger interaction betweenthe dipole moment of the ethyl radical and the quadrupole moment of CO2 (see thesolvent model of Vujosevic et al.92). Cormier et al. propose that at a density ofB0.4 g cm�3 there is clustering of the CO2 molecules around the ethyl radical and thatthe effective local density is closer to B0.6 g cm�3, an increase of 50%, but furtherexperiments are needed to confirm this result. The other radical to have been studiedis the MuH2C–CF2 radical, which was produced by the reaction of Mu with vinylidenefluoride, and whose identity was confirmed by measuring Am using TF-mSR.145

8 Radicals in zeolites

Zeolites are aluminosilicate structures incorporating charge- compensating cationsthat have a ubiquitous presence as molecular sieves and heterogeneous catalysts inchemical industry. The host–guest interactions and the mobility of reactants,intermediates, and products of reactions in zeolites are of paramount importancefor the performance of catalytic processes. Nevertheless, relatively little is known atthe microscopic level about the interactions of guest molecules in different zeoliteframeworks, particularly in the case of neutral free radicals that might be formed,in situ, by H-atom addition reactions from active sites, in analogy with the commonlyexpected formation of carbocation intermediates by protonation from Bronsted acidsites. EPR studies of radicals in zeolites are limited by the need for a sufficiently largeconcentration of radicals needed for their detection, which means that the radicalsmust be comparatively long-lived and hence immobile or else chemically stable like2,2,6,6-tetramethyl-1-piperidinyloxy (Tempo). Radicals are mobile under catalyticallyrelevant conditions and this leads to termination reactions and the loss of the EPRsignal, which in practice limits EPR studies of radicals in zeolites to low tempera-tures. H-adduct radicals formed by radiolysis of olefinic and aromatic hydrocarbonguests in zeolites have been observed by EPR at low temperatures.146 mSR can be usedto study radicals over a wide temperature range, as there are only a few radicals in thesample at one time. The Roduner and Fleming groups have studied a large numberof muoniated radical species in different zeolite frameworks over the last 20 years.


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Experiments have been mainly performed on two types of zeolite framework;ZSM-5 and faujasites (X, Y and USY). The cation is specified in front of theframework type. The ZSM-5 zeolite is composed of several pentasil units linkedtogether by oxygen bridges to form pentasil chains. A pentasil unit consists ofeight five-membered rings where the vertices are Al or Si and an O bondedbetween the vertices. The pentasil chains are connected by oxygen bridges to formcorrugated sheets with 10-ring holes, with Al or Si as vertices and an O bondedbetween each vertex. Each corrugated sheet is connected by oxygen bridges toform a structure with straight 10-ring channels running parallel to the corruga-tions and sinusoidal 10-ring channels perpendicular to the sheets. The estimatedpore size of the channel running parallel with the corrugations is 5.4–5.6 Å. Thefaujasite framework consists of sodalite cages which are connected throughhexagonal prisms. The pores are arranged perpendicular to each other. The pore,which is formed by a 12-membered ring, has a relatively large diameter of 7.4 Å.The inner cavity has a diameter of 13 Å and is surrounded by 10 sodalite cages.The X, Y and USY zeolites have the same structure but differ in the Si/Al ratio.

Roduner et al. studied the reorientation dynamics of C6H6Mu radicals inNaZSM-5 with SiO2/Al2O3 ratios of 670 and 900 and loadings of one and twobenzene molecules per unit cell using ALC-mSR (Fig. 26).147 The width of theresonances at room temperature is much less than in the static limit, indicatingconsiderable motion. Modelling of the ALC resonance lineshape indicates that theC6H6Mu radical rotates rapidly about the axis perpendicular to the molecular planeon a critical time scale of 50 ns as well as jumping between different sites with

Fig. 26 (a) ALC-mSR spectra obtained with benzene at a loading of one molecule per unit cell onZSM-5/900 at various temperatures. The top entry is a simulation based on isotropic coupling constantsof 529.5 MHz for the muon and 122 MHz for the proton and for the rhombic dipolar contributions of aradical in the absence of any dynamics. The background has been subtracted from the ALC-mSR spectra.(b) Axial anisotropy of the muon hyperfine interaction as a function of temperature for the cyclo-hexadienyl radical at a benzene loading of one molecule per unit cell in ZSM-5/900 (squares) and of twomolecules per unit cell in ZSM-5/670 (circles). The line corresponds to a fit of a reorientational two-sitejump model for points below 300 K. The inset shows the ZSM-5 structure with a benzene moleculeroughly to scale at a channel intersection. The zigzag channels are drawn in the horizontal and thestraight channels in the vertical direction.147


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orientations that differ by an angle of 1101 and 1.0 kJ mol�1 in energy. The radicalwas mobile down to 50 K, which indicates that the radical is located at the channelintersections, while the side channels become accessible above 450 K. The C6H6Muradical behaves very similarly to benzene in ZSM-5 although the critical time scaleprobed by mSR is different from that of other spectroscopic techniques.

ALC-mSR has provided evidence that the muoniated cyclohexadienyl radical forms acomplex with the diamagnetic Cu+ cations in CuZSM-5.148 The D1 and D0 methyleneproton resonances of the cyclohexadienyl radical were much broader than in high-silica ZSM-5, indicating considerably less motional averaging. An additional intensebroad peak was assigned as being two overlapping D0 for two copper isotopes(63Cu and 65Cu). The positions of the peaks indicate that only a small amount ofspin density (2.7%) is transferred to the Cu+ cation and that the structure of thecomplexed cyclohexadienyl radical is affected very little by the interaction with thecation. Additional resonances in LiZSM-5 and NaZSM-5 suggest that the cyclo-hexadienyl radical can also form complexes with Li+ and Na+ cations.149

The ALC-mSR spectra of benzene-loaded HZSM-5/50 zeolite suggest that theC6H6Mu radical is transformed into another species at low temperatures.150 Aroundroom temperature, the D1 and D0 methylene proton resonances occur at similarfields to the corresponding resonances in high-silica ZSM-5 but are much broader,indicating a stronger interaction between the radical and the zeolite. Two additionalresonances were observed as the temperature was lowered, while the originalresonances decreased in intensity and finally disappeared below B140 K. Theadditional resonances were assigned to the C6H7Mu+ radical cation, which wasformed by the protonation of the ortho-carbon of the muoniated cyclohexadienylradical and indicates that the zeolite is more acidic at lower temperatures.

McKenzie et al. studied the muoniated azacyclohexadienyl radical isomers thatwere produced by the addition of muonium to pyridine in high silica ZSM-5zeolite (Si/Al = 450) and in liquid pyridine at 298 K using ALC-mSR.151 Thehyperfine coupling constants of the azacyclohexadienyl radicals are similar inboth environments, which indicates that the radicals do not interact strongly withthe zeolite framework and the relative yield of the three radicals was found todepend on the medium, with the yield of the para isomer being six times larger inZSM-5 than in pyridine. The difference in relative yields suggests that even a weakinteraction with the zeolite framework can effect the reactivity.

The ALC-mSR spectrum of C6H6Mu radicals in NaY zeolite152,153 with loadings of2–3 benzenes per supercage (SC) is very different from that of benzene-loaded ZSMin that there are four broad resonances, three of which are D1 and the remainderbeing a D0. The assignment was confirmed using TF-mSR spectroscopy. Two of theD1 resonances correspond to different orientations of the CHMu methylene groupwith Mu pointing away (exo) or toward (endo) the SII Na cation. The interaction withthe Na cation gives rise to unprecedentedly large (20%) shifts in hyperfine couplingconstants, indicating that a strong bond is formed with the p electrons of theC6H6Mu radical. The endo- and exo-orientations of the C6H6Mu radical give rise totwo different muon hfccs because coupling to the Na+ distorts the cyclohexadienylradical from planarity and causes the muon and the methylene proton to beinequivalent. The third D1 resonance is due to adsorption of the radical at thewindow sites between the supercages. The width of the resonances and the absenceof significant temperature dependence indicate that the motion of the radical is


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extremely limited. The cyclohexadienyl radical is essentially frozen on the timescale of 50 ns, complexing the SII Na+, which is unlike the behaviour of the benzenemolecule in NaY and other faujasites where there is clear evidence for rotationabout the C6 axis as well as long-range diffusion from 2H NMR spectra. This hasbeen explained by the electric dipolar interaction of the C6H6Mu radical with thezeolite framework.154,155

Recently Fleming et al. have studied the C6H6Mu radical in NaY, HY and USY,over a range of loadings and temperatures.156 The ALC-mSR experiments onC6H6Mu radicals in NaY zeolite found that there was little or no loadingdependence on the hfccs or the ALC line widths, and confirms the conclusionsof the earlier analysis of a distorted nonplanar C6H6Mu radical due to stronghost–guest interactions with extra-framework sodium cations (Fig. 27). Thepopulation of C6H6Mu radicals at the window sites increases for higherloadings. The observation of D1 resonances up to 471 K indicates that there islittle motion on the timescale of B50 ns and that the sodium ions in NaY act aseffective traps for cyclohexadienyl radicals. The results were substantiallydifferent in HY and USY where a pronounced loading dependence wasobserved. In HY at a loading of 2 benzenes per SC a D1 resonance and a D0

resonance of a largely planar C6H6Mu radical in a polycrystalline environmentwere observed over the whole temperature range, both above and below the bulkmelting point of benzene. The magnitude and temperature dependence of thehfccs indicate that there is a very small amount of spin density transfer fromthe radical to OH binding sites and some slight distortion from planarity. In theALC-mSR spectra of C6H6Mu radicals in USY zeolite with loadings of 2 benzenesper SC the D1 resonance broadens dramatically above B310 K due to isotropic

Fig. 27 Schematic diagram of the C6H6Mu radical interacting with the SII cation in NaY (shown by thegreen circle), which causes distortion from planarity of the C–Mu bond above (exo) and below (endo) theplane, shown in the diagram as Hexo and Hendo, respectively. The Si atoms are shown by the light graycircles, with the O–atom bridges shown by the smaller red circles. Atom sizes are not to scale.156


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reorientation of the radical within the USY SC with a correlation time estimated tobe B0.1 ns. Very similar behaviour is seen in the USY and HY zeolites withloadings of 4 benzenes per SC at comparable temperatures, but an additionalresonance is observed at low temperatures in USY with 4 benzenes per SC and thisis believed to result from benzene in intergranular regions. In USY with loadingsof 6 benzenes per SC benzene resides primarily in intergranular regions.

The muoniated ethyl radical has been observed in NaY, HY, and USY zeolites byTF-mSR and ALC-mSR and the muon and proton hfccs have been measured over awide range of temperatures.157 One D1 and two D0 resonances were observed,which indicates that the ethyl radical resides at only one site in all three faujasiteframeworks, unlike the C6H6Mu radical in NaY, where it sits at several sites. Thehfccs of the ethyl radical are larger in the faujasite zeolites compared with thebulk phase and this was interpreted as resulting from the ethyl radical bindingwith the SII cation sites in NaY and the surface hydroxyl groups in HY and USY.The temperature dependence of the hfccs is similar in the bulk and faujasitezeolites, which indicates that binding of the ethyl radical has very little effect onrotation about the C–C bond. The linewidths in the TF and ALC spectra increasedramatically with increasing temperature, and this is assumed to result eitherfrom the radical desorbing from the zeolite framework or jumping betweenequivalent sites, with an activation barrier of 20 � 5 kJ mol�1. The isotropic hfccsagree well with values from DFT calculations.158

9 Conclusions

In this review it has been demonstrated that mSR can be used for studying the structureand dynamics of radicals in a range of environments and that by studying the in situproduced muoniated radicals it is possible to learn about the behaviour of complexmaterials. It is important to include a word of caution as mSR is not appropriate for allsystems and great care must be taken to consider the strengths and weaknesses of mSRbefore beginning a research project. Muons can be implanted into any material butthat does not mean that useful information will come out. Under the right circum-stances however mSR can have advantages over the traditional spectroscopic techni-ques used to characterize radicals such as EPR and provide unique information. Thereare many areas that are amenable to study by mSR that have not yet been examined,so there are fantastic opportunities for the interested researcher.

Acknowledgements

I wish to thank all of my colleagues who have made working in this field soenjoyable. In particular I must thank (in alphabetical order) Greg Chass, JasonClyburne, Stephen Cottrell, Don Fleming, Khashayar Ghandi, Sean Giblin, UpaliJayasooriya, Paul Percival, Emil Roduner, Zaher Salman, Robert Scheuermann,Kamil Sedlak and Alexey Stoykov.

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The positive muon and μSR spectroscopy: powerful tools for investigating the structure and dynamics...

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