Modern EPR-Related Methods in Surface Science and Heterogeneous Catalysis*

©byR.Oldenbourg Verlag,

-0044-3336/87

Modern EPR-Related Methods

in

Surface Science and

_{Heterogeneous}

_Catalysis*

By

M.

_Heming

Physikalisch-Chemisches

Institut derUniversität,

Winterthurerstrasse190,CH-8057Zürich,Switzerland (Received July22,1986)

Electron

_spin

resonance

/

Electron nuclear doubleresonance

\

Muon

_spin

rotation

_{/ Surfaces}

Materials of interest in

_{heterogeneous catalysis}

arealmost

exclusively

ina

polycrystalline

oramorphousstate. In EPRspectroscopy,orientationalaveraging, inhomogeneousline broadeningandoverlapofspectraoften leadtoadrastic loss of resolution. Thismight preclude detailed information about the observed species and its interaction with the surroundings.Theapplicationof various modern ENDOR andpulseEPR

_techniques

in orderto_improvethe resolution is discussed. In addition, thecloselyrelated method of

Muon

_Spin

RotationO^SR)is considered in view of itspossiblecontributionstothe

_study

ofMuonium,the

_{light isotope}

of

_hydrogen,

and muonium-labeledorganicfree radicals

onsurfaces.

Katalytischinteressante Materialienliegen

häufig

nurinpolykristallineroderamorpher

Formvor. Dementsprechendsind diezugehörigen EPR-Spektrenin derRegelalsFolge

der räumlichen Mittelung sowie einer starken inhomogenen Linienverbreiterung und eventuell einer

_{Überlagerung}

verschiedenerSpektrennurschlechtaufgelöst.Die

Anwen-dung verschiedener ENDOR- und EPR-Puls-Methoden zur

Verbesserung

des

Auflö-sungsvermögens wird diskutiert. Zusätzlich wird die

Myonen-Spin-Rotations-^SR)-Technik diskutiert. Mittels dieser Methode können Myonium (das leichte _Isotop des

Wasserstoffatoms)undMyonium-substituierteRadikale auf Oberflächen untersucht

wer-den.

1. Introduction

Withinthe last_{30 years EPR has}becomea

powerful

and

indispensible

tool for the

_study

of

_{paramagnetic species}

in

_{heterogeneous catalysis}

and surface science

_[1

—

5].

In

_principle

EPR is

_capable

of

_delivering

information

concerning

the nature of

paramagnetic species,

their electronic and

* _{Presented as a}

Plenary

Lecture atthe IV. International

_Symposium

on

Magnetic

Resonance in Colloid and InterfaceScience, Münster, FRG,July21—25,1986.

geometrical

structure,theirinteraction with the

_{surroundings,}

their

reactivi-ty

and kinetics. Anaccuratecharacterizationofa

paramagnetic species

and

of the interaction with its

_surroundings

isa formidable task. It

requires

the

determination ofasmanyas

possible Spin-Hamilton

_parameters,

including

the orientation of the

_principle

axes of the various tensors. In addition a

careful

_analysis

of the

_lineshape

isnecessary toelucidate

_dynamical

_aspects

[6,

7],

and kinetic studies may involve time-resolved EPR

techniques

on various levels of

_{sophistication.}

An idealEPR

_experiment

therefore

_requires

a well-defined

_system,

_e.g. a

single-crystal

surface.

Although

very few

experiments

have been carriedouton such

systems

(e.g. [8]) demonstrating

the

_capacities

ofEPR

_{spectroscopy,}

the

_overwhelming

_majority

of materials in

_{heterogeneous catalysis}

isina

polycrystalline

or,evenworse,

amorphous

state.

_Therefore,

the determination of the orientation of the

_principal

axes

of the various tensors is a

priori

not

_possible.

Orientational

_averaging

of the

_anisotropie

interactions,

distribution of

_{Spin-Hamilton}

_parameters

rather thanwell-defined

values,

and

_{inhomogeneous}

line

_broadening

as a consequenceof weak

dipolar

interactions often resultin a

poorly

resolved

EPR

_spectrum

andmakea

meaningful quantitative

analysis

difficult,

ifnot

impossible.

Additional

_{complications}

_mayarise

_through

extensive

_overlap

of

_spectra

ofdifferent

_species.

Inthecaseof

inhomogeneous

line

broadening

aconsiderable resolution

enhancement can be achieved

by

applying techniques,

which are

capable

of

_{directly measuring}

NMR transition

_frequencies

in

_paramagnetic

_systems.

It is _{the purpose} of _{this paper} to discuss with this

_respect

the

_possible

applications

ofmoreadvanced EPR

techniques,

like the various forms of

Electron Nuclear Double Resonance

_(ENDOR)

_spectroscopy

_[9

—

11]

and Electron

_Spin

Echo

_(ESE)

_spectroscopy

_{[12, 13],}

the

_pulse

variant ofcw

EPR. In

addition,

the

_closely

relatedmethod of Muon

_Spin

Rotation

_(pSR)

[14]

will be discussed in view ofits

_potential

contributions to the

_study

of

Muonium,

the

_{light isotope}

of

_hydrogen,

and muonium-labeled

_organic

radicals on surfaces.

2. Electron nuclear double

resonance

In an ENDOR

experiment

one

simultaneously performs

an EPR and a

NMR

_{experiment by observing}

the effect of a

_strong

radio

frequency

(rf)

field on a

partially

saturated EPR

absorption.

The

technique

and its

applications

havebeen

_extensively

covered in recent

_monographs

_[9

—

11].

ENDORonmaterialsinadisorderedstate_may

_give

riseto twodifferent

types

of

spectra

[9, 15]: (1) anisotropie

ENDOR,

i.e.

_frequencies

do occur

displaced

from the free nuclear

_{precession frequency,}

and

₍₂₎

Matrix

ENDOR,

which often constitutes ofa more or less structured

signal

cen-teredat thenuclear Larmor

_frequency.

36

2.1.

_Anisotropie

ENDOR

The

_shape

of the

_spectrum

_depends

_{characteristically}

on the

_part

of the EPR

_spectrum

which is

saturated,

on the

degree

and kind of

anisotropy

and on the dominant relaxation

pathways.

It is the latter

fact,

which may

complicate

asimulation of the

lineshape considerably.

Rist and

_{Hyde [16,17]}

first

_pointed

outthe

_possibility

toobtain ENDOR

spectra

which

_{correspond only}

to a limited set of

_{orientations,}

if the ENDOR effect is observed at the

_turning

_points

of an EPR

_spectrum.

Specifically, they

noted that it is

_possible

to obtain

single-crystal

_type

spectra

for

_systems

where

(1)

one

magnetic

interaction

(hyperfine anisotropy,

zero-field

splitting

or

g-anisotropy)

dominatesthe EPR

_spectrum

or

(2)

two

_magnetic

interactions havea

comparable degree

of

anisotropy,

but theaxesof

largest anisotropy

coincide.

Asan

example

of

(2),

the EPR and ENDOR

_spectra

of

VO2

+ adsorbed onNaY

[18]

areshown in

Fig.

1a,b. The zeolite is ina

fully hydrated

state.

In the EPR

_spectrum

no

hyperfine coupling

with

neighbouring

nuclei is

observed. With the

_magnetic

field set at the mx =

— ß\\

transition,

only

orientations

_along

the common z-axes of the g- and the

V02

_+-hyperfine

tensorare selected. The ENDOR

_spectrum

is

readily

identified to be due

to

VO(H20)2+

_{by comparison}

with the frozen solution

_spectrum.

The

frequencies

correspond

to the

_hyperfine

tensor

_components

ofthe "axial" and

_"equatorial"

_protons

_along

the V=0 bond direction. On the other

hand,

a

quasi

two-dimensional

_spectrum

is obtained withthe

magnetic

field

set at the

_Mj

=

—

3/2x

transition,

as shown in

Fig.

lc. In addition to

260 300 3W 380mT 10 15 20MHz

Fig. 1.(a)EPR_spectrumof the

_{VO(H20)5+-complex}

in

_fully

hydrated NaY. A

single-crystal

like ENDOR spectrum (b) is observed with themagnetic field set attherti\ =

—

7/2ytransition.Forthe

magnetic

fieldset atthem¡=

—

3/2±transitiona

_{predominantly}

two-dimensional ENDOR_spectrum(c)is obtained.

_Signals

dueto_protonsin the axial

watermoleculearedenotedas Hax._{vp markes the free nuclear}

_{precession frequency.}

No Matrix-line is observed.Redrawn from Ref._[18]withpermissionof the author.

the

_{perpendicular (relative}

to the V=O bond

direction) hyperfine

_tensor

components

of the axial

_protons,

the

_spectrum

reveals the

_parallel

_(very

weak)

and

_{perpendicular}

_components

of the

_equatorial

_protons.

Evacu-ation atroom

_temperature

leadstoa loss of the

_proton

signals,

which has

been

_interpreted

intermsof

_binding

of

V02+

to_{four oxygens of the zeolite}

network and loss of the axial watermolecule.

Inordertoobtainthe true

_principal

values of the

_hyperfine

tensoritis

necessary to record the ENDOR

_spectrum

overthe entire EPR

_spectrum

[19,

20].

A

_theory

of

_{polycrystalline}

ENDOR

_patterns

for _dominant

g-anisotropy

[19]

revealsthat it is not

_{only possible}

to extract the

_principal

values of the

_hyperfine

tensor,but that in addition the relative orientations of theg-and -tensors may be deduced fromextra

_divergences

and maxima

inthe ENDOR

_spectrum

atintermediate field

_settings.

Alternatively,

some of the

principal

values of the

hyperfine

tensorand the orientations of their

_principal

axes may be obtained from ENDOR-induced EPR

_spectra

_[21].

The idea is to measure the

changes

of the

amplitude

ofan ENDOR

frequency

= _vn + _{as a} function of the

magnetic

field. Fora

single

coded

(frequency

modulation

only)

ENDOR

line the EPR

_spectrum

is

_readily

obtained in the form of an

absorption

spectrum.

For =

1/2

^max(m¡n),

_a

single-crystal

type

EPR

spectrum

is

obtained. Since the

_frequency

is field

_dependent

one has to

_adjust

the rf-fieldwhilst

_scanning

the

_magnetic

field.

In contrast to the orientation selected ENDOR

_spectra,

_powder

_type

spectra

are obtained for

arbitrary

magnetic

field

settings

or whenever conditions

₍₁₎

and

₍₂₎

are not fullfilled. In

_general,

the ENDOR

_intensity

will be the better the lower the

_{hyperfine anisotropy}

is.

Thus,

j?-couplings

of

_organic

free radicalsare

usually quite

wellresolvedsincetheir

anisotropy

constitutes often

_only

asmall fractionof the

isotropie hyperfine coupling.

In _contrast,

_signals

due to

_-protons

are often smeared out over a

large

frequency

range and difficultto detect

_{[9, 15].}

Indeed,

theease with which it is

possible

to measuresmall

ß-couplings

accurately

has enabled Clarkson

_[22]

to show that the

_^-couplings

of the

perylene

cation radical adsorbed on metal oxide surfaces can be used to

monitor the interaction

_strength

ofthe radical with the acidic

_adsorption

sites. The

_^-couplings

werenotresolved in the EPR

_spectra.

So

far,

we

implicitly

assumed thecrossrelaxationrate

(T~l)

to be slow

compared

to the electron and nuclear

_spin-lattice

relaxation rates

(T[el,

Tfn1).

If,

however, Tx

<

Tle, Tln

atrue

_powder

_pattern

is

_obtained,

i.e. all

possible

orientations contribute

_irrespective

of which

_part

of the EPR

spectrum

is saturated. Thiscase has been treated

by

Dalton and Kwiram

[23].

Under this condition ENDOR-induced EPRmaybe usedto

_separate

overlapping

EPR

_spectra.

In the last few years

Schweiger

and coworkersintroduced a number of

spectra.

Among

them,

ENDOR

_utilizing

a

circular-polarized (CP-ENDOR)

[24]

or a

polarization-modulated (PM-ENDOR) [25]

rf-field should turn outtobe useful for the

_{interpretation}

of

_anisotropie

_spectra

too.

In CP-ENDOR one takes

advantage

of the

fact,

that the transition

probability

induced

_by

the left hand

_(Lh.)

or

right

hand

(r.h.) rotating

rf-field

_component

_depends

ontherelative

magnitude

of theexternal

magnetic

field

B0

(I)

and the internal

_magnetic

field

_Be

_(\).

If

_B¡.

_outweights

B0

than the direction of the effective

_magnetic

field

_Befi

_{(|") changes}

its

_sign

with

For this

_simplified

_example

of

_{isotropie couplings}

_(a,

g„ >

₀₎

_only

r.h.

(Lh.)

rotating

field

_components

induce transitions for_ms =

+1/2

(—1/2).

On the other

hand,

in PM-ENDORa

rotating

rf-fieldcauses a

modula-tion of the transimodula-tion

_amplitude.

The modulation

_depth

decreases with the

_hyperfine

interaction.

_Thus,

PM-ENDOR is a

technique

suitable to

suppress the Matrix-line. 2.2. Matrix-ENDOR

Besides the

_anisotropie

linesa commonfeature in the

_spectra

of disordered

materials is the so-called Matrix-line

_{[26] occurring}

at the free nuclear

precession

frequency.

This line is dueto

_{weakly coupled}

nuclei,

themain interaction

_being

the electron-nuclear

_dipolar

interaction. As an

example,

the Matrix-line

_originating

from the interaction between the

KgH

surface defectcentreinthe

_{MgO (111)}

_crystal

face and

_physisorbed

H2

at4.2 is shown in

_Fig.

2

_[27].

An_{average interaction distance of}

_<r>

= 0.52_nmhas

been inferred from the line-width.

A

_{quantitative analysis}

ofthe

_{lineshape following}

the ideas of

_Hyde

and coworkers

_{[26, 28]}

is,

in

_general,

tedious and does not

_{always provide}

a

unique

set of

_parameters

_[15].

The

_lineshape

is

_particularly

sensitive to

the nuclear relaxation mechanism. Given aS =

1/2,

/ =

1/2 spin

system

aPake doublett would be

expected

foran

isotropie

nuclear relaxation rate

Ti„.

However,

assuming

that the nuclear relaxation occurs

primary

through

the modulation of the electron-nuclear

_dipolar

interaction via the

relaxing

electron

_spin,

_^1

becomes orientation

_dependent

and the doublett

mergesintoa

singulett

[26].

Withinthelast few years it turnedoutthat the

analysis

of the modulation effectin ESE

_spectroscopy

is better suited to

obtain structuralinformationsfrom_very

_{weakly coupled}

nuclei

_{[12, 13].}

3. Electron

_spin

echo

_(ESE)

_spectroscopy

InanESE

experiment

onemonitorsthe

spontaneous

outburstof microwave energyas afunctionof the

timing

oftwoor moreshortresonantmicrowave

-1-

13 15 17 MHz

Fig.2. ENDORsignalofthe K§Hsurfacecentrein_MgOafteradsorptionofH2at4.2 .

Redrawn from Ref. _[27]withpermissionof the author.

Fig.3. Schematic of the 2

_pulse

Electron

_Spin

EchoModulation

_experiment.

pulses.

In a

two-pulse

experiment,

the initial

/2

pulse

_prepares the

spin

system

in a coherent state.

_{Subsequently,}

the

_spin

_packets,

each characterized

_by

itsownLarmor

precession frequency

_a>¡,startto

_dephase.

A second

_-pulse

at time

_effectively

reverses the time evolution of the

spin

packet

magnetizations,

i.e. the

_{spin packets}

start to

_rephase,

and an

emission of microwave energy

(the

primary echo)

occurs at time2 . The

echo

_amplitude

as a function of constitutes the ESE

_spectrum

(Fig. 3).

40

Relaxation processesleadto anirreversible loss of

phase

correlation,

thus

the

_{amplitude decays}

withacharacteristic time

T™,

the

phase

memorytime.

Fortunately,

the

_decay

is often

_accompanied

_by

amodulation of the echo

amplitude. Analysis

of themodulation

_frequencies

and

_amplitudes

forms the basis of the Electron

_Spin

Echo Modulation

_(ESEM)

_{spectroscopy.}

The modulation effect is a consequence of the violation of the

high

field

approximation.

Non-diagonal

elements due to

_{anisotropie hyperfine}

and

quadrupole

interactionscause

mixing

of nuclear levels. This inturnallows the simultaneous excitation of allowed and forbidden

_transitions,

if the microwave

_magnetic

field is

_strong

_enough.

The

_branching

oftransitions

causes

interferences,

which manifest themselves as a modulation of the

echo

_amplitude.

A convenient

_expression

intermsofthe

_{eigenfunctions}

and

eigenvalues

ofa

spin

systemunderthe

assumption

of

complete

excitation of

the EPR

_spectrum

has been

_given

_by

Mims

_{[29, 30].}

Fora S=

1/2,

/=

1/2

system

the modulationfunctioncan _{be written} as

[29]

:

Vmod(2 )

= 1 —

k/4[2

— 2cosovr — 2_cosco^r

_(la)

+

_cos(cox

—

(Op)T

+

_cos(a>a

+

_{ß) ]}

k =

/ ß

_, =

ggjßn(3

sin0cos0)//zr3

(1

b)

^ß are the ENDOR

frequencies,

_iui is the nuclear Zeeman

frequency,

the

_angle

between the

_magnetic

field

_B0

and theelectron-nuclear axis. All other

_symbols

have theirusual

_meaning

in

_magnetic

resonance.In

deriving

Eq.

(1)

the

_validity

of the

_{point-dipole approximation}

and an

isotropie

g-factor have been assumed.

The

_frequency

_spectrum

contains not

_only

the ENDOR

_frequencies,

but inaddition their sumsand differences. For

weakly

coupled nuclei,

_ß

= , and

only

two

frequencies

are observed. In the presence of

in-teracting

nuclei the total modulation function is

_simply

the

_product

ofthe individualmodulation functions

_{[29, 30]}

:

Vmod Hi

mod

·

(2)

From

_{Eqs. (1)}

and

₍₂₎

it is evident that the modulation

_depth

increases

strongly

with the number of

_interacting

nuclei and a

decreasing

electron-nuclear distance. In

addition,

the modulation

_depth

also increases with the nuclear

_spin

/

_[29].

_However,

it has to be recalled that close and therefore

strongly interacting

nucleiareESE-silent. Indisordered matricesa simula-tion of the ESE

_spectrum

_requires,

in

_principle,

a

geometrical

model for

the mutual

_arrangement

of the

_interacting

nuclei. On the other hand it is the aimofthe

_experiment

toestablish suchamodel.

Consequently,

Kevan etal.

[31] argued

to base the data

_analysis

on a

spherically

uncorrelated distribution

_model,

i.e.

Cu:Si02IC2DL

2 Pulse ESE

O 2 µ5

Fig.4. Calculated (-) and experimental (-) 2

_pulse

ESEM spectra for impregnatedCu:Si02activatedat1000 andwithadsorbedC2D4.Theproposedmodel for theCu2+

—

C2D4interaction is showntoo. Redrawn from Ref.[33] with

_permission

from L. Kevan.

where r is an effective shell distance. This model is now

widely

accepted

[32].

A fit reveals three

_parameters,

the number of

_interacting

nuclei,

their effective distance and the Fermicontact interaction.

Asan

example

the

two-pulse

ESE _spectrum for

impregnated

Cu2+ in a silica

gel

activated at 1000 with

_subsequently

adsorbed deuterated

ethylene

is shown in

_Fig.

4

_[33].

The

_analysis

indicates four deuterons at

r = 0.33 nm and with _űiso = 0.15 MHz. At this distance _a direct bond

between

Cu2+

and

_ethylene

is

_clearly

excluded.

_Together

with the informa-tion derived from the

_g-factors,

the authorswereabletoproposeadetailed

geometrical

model,

which is shown in thesame

figure.

Inessence,the Cu —

04

tetrahedra distortupon

adsorption

of

ethylene

towardseithera

trigonal-bipyramidal

or a

square-pyramidal

_geometry.

Instead of

_stepping

from

_experiment

to

_experiment

the full informa-tioncanbe obtained in a

single

_step

by

replacing

the initial

/2-pulse

with

a low-level extended-time

excitation,

_e.g. a cw-microwave

magnetic

field

withconstant

_amplitude

and

_{appropriate frequency}

_[34].

_However,

onehas

to takesome

sensitivity

lossinto account.

The mainlimitationofthe

_two-pulse

_{experiment originates}

from

_phase

relaxation _{processes. If} becomestoo short the instrumental dead

_time,

typically

about 150ns, maycover asubstantial

part

of the ESE

spectrum.

Further,

multiple frequencies complicate

the

_spectrum.

Both

_problems

may

be overcome

by

observing

the stimulated echo in a

three-pulse

_sequence.

Dividing

the second

_pulse

of the

_{two-pulse experiment}

into two

_/2

_pulses

essentially

storesthe

_{magnetization}

inthe

—

direction.The echocannow be followed over a time of the order of

magnitude

7\

>

T™.

With the

separation

between thefirstand the second

_pulse

denotedas and theone between the second and thirdas T,the stimulated

echo,

occurring

at2 +

,

is monitored in the

-space.

The modulationfunctioncanbecalculated

from

_{Eq. (1) [30]:}

^

=

1/2^,70+^,70].

(4)

Incontrastto the

_two-pulse

modulation function the sumsanddifferences of the ENDOR

_frequencies

are now eliminated. Maximum

modulation-occurs for

_weakly

interacting

nuclei for =

(2

+

1) ,

whereas for

( \ = 2 the modulation

amplitude

vanishes. In

general,

the

three-pulse experiment

is

_superior

tothe

_{two-pulse experiment.}

_However,

several

experiments

with different

_settings

have to be

_performed

to make sure thatno

frequencies

areoverlooked.

Alternatively,

the properselection of

maysuppress unwanted

frequencies

and

simplify

the

analysis.

Fig.

5 shows the

_three-pulse

ESE

_spectrum

of

Pd+

in

_Pd17-NaX

formed after methanol

_{adsorption [35]. Selectively}

deuterated methanol was used inordertodetermine the orientationof theadsórbatewith

_respect

toPd+

.

interaction withonemethanol molecule andamolecular

dipole

orientation.

Pd+

is

_probably

locatedatSII'or SII sites in the sodalite cages.

Several

_glitches

in the

_spectrum

are

apparent

and

disturbing. They

originate

from

_two-pulse

echoes

_(at

times =0 and

= )

and from _a

refocussing

echo with

_{opposite phase}

attime2 .

Recently,

Fauthetal.

_[36]

demonstrated a

phase-cycling

excitation

method,

which eliminates these

unwantedechoes.

The full

_potential

of ESEM spectroscopy has been demonstrated

_by

Kevan and coworkers

_{[37, 38]}

in a

continuing

series of

investigations,

concerning

the

location,

migration

and coordination of transition metal ionsonmetal oxide surfaces.

Besides the

_study

of modulation

effects,

ESE canbe useful to sort out

overlapping

EPR

_spectra

and for the

_study

_{of slow motional processes. For} the

_separation

of

_overlapping

EPR

_spectra

onetakes

advantage

of the

time-domain nature of ESE.

_Keeping

in a

two-pulse experiment

fixed and

sweeping

B0

produces

anESE-induced EPR

_spectrum

as

long

asthe

phase

memory time is field

independent.

The induced EPR

spectrum

is

_displayed

as an

absorption

_spectrum.

Bx

has to be reduced

_compared

to ESEM to

allowa

good

resolution of theEPR

_spectrum

andtoavoidanymodulations.

Overlapping

EPR

_spectra

may

easily

be

separated,

if the two

_{(or more)}

paramagnetic

species

exhibit

_sufficiently

different

_phase-memory

times,

_by

properselection of . On the other

hand,

significantly

slower motionscan

be studied

_by

ESE,

since the

_phase

memory time canbe several orders of

magnitude higher

than

_?,

the inverse of the

_{inhomogeneously}

broadened

EPR line. In

_addition,

the

_{spin packet}

line-width can be monitored over

the entire EPR

_spectrum

in atwo-dimensional

experiment providing

very

detailed information about motionalprocesses

_[39].

4. Muon

_spin

rotation

Although

chemists have

_appreciated

fora

long

time the role of

elementary

particles,

such as the

electron,

the

_proton

or the neutron, in studies

con-cerning

the structure and

_dynamics

of matter, other

elementary particles

arestill

regarded

as

being

to some extent"exotic".

To

_begin

with,

it thereforeseems

appropriate

tointroduce in brief the

positive

muon and to

emphasize

its usefullness as a

spin probe

from the

point

of view ofachemist

[40].

The

_positive

muonis

produced

in the

parity-violating decay

ofa

positive

pion

into amuon anda neutrino:

+

-> _µ+ + _µ .

Like the

_proton

it is a

spin

1

¡2 particle.

However,

its associated

magnetic

momentis3.18 times

_larger

thanthe

_proton

_magnetic

_moment,whereas its

mass is smaller

by

a factor of9. It isa short-lived

particle

(i1/2

= 1.5

µß)

and

_decays

intoa

positron

and twoneutrinos. Whenamuon is

_stopped

in

matteritthermalizeswithinlessthan1 ps.

_During

this timeitcanassociate

withanelectron.

Thus,

Mu

(sii

+

_e~)is

formed,

which shouldbe

_regarded

as _the

_light

isotope

_of

hydrogen

(=p+e~).

_Indeed,

_{the Bohr}

_radius,

_the

reducedmassand theionization_energycoincide_{within less than 0.5%. As}

an

isotope

of

H,

Mu behaves

chemically

(besides

asometimes

hughe

isotope

effect)

very much alike. Mucan

undergo

a

variety

of

reactions,

including

theadditionto anunsaturated bond:

Thereby

amuonatedradicalisformed.

Muoniumandmuonatedradicalshavebeen

_mainly

studied

_by

the time-domain

_technique

ofMuon

_Spin

Rotation

_^SR).

This

_technique

has been

very

successfully exploited

for

_[41]:

(1)

Studies of the kinetics of Mu reactions in the gas

phase

and the

liquid

phase.

Especially,

thegas

_phase

studies have

_provided

a_{very critical}

testing

ground

for reactionrate theories.

(2)

Thedetermination ofabsoluterate constantsoffast

_organic

radical reactionsin the

_liquid

_phase.

Inthiscasethemuon is usedas a

passive spin

probe.

The

_{µSR-technique}

is outlined in

_Fig.

6.

_{Spin-polarized}

muons are

stopped

ina

probe,

whichitselfis

placed

ina

magnetic

fieldtransversewith

respect

to the

_{spin polarization}

of the

_incoming

muons. The muon

spin

then starts to _{precess with} a

frequency depending characteristically

on

the

_{locally experienced magnetic}

field. The evolution of the muon

spin

polarization

in time andspaceis monitored

by

_measuring

the

time,

which the muon

spends

in the

probe

until it

decays,

and the direction of the emitted

_positron.

The latter is

_preferably

emitted

_along

the instantaneous direction of themuon

spin.

The

technique requires

that

only

one muonat

atime is_presentin the

probe. Summing

upevents

_(typically

afew

million)

for a

given

direction

yields

radioactivemuon

decay

curves, modulated

_by

muon

spin

_{precession frequencies.}

Analysis

ofthesecurves inthe Fourier

space

[42],

reveals these

frequencies (hyperfine

couplings),

their

amplitudes

(yields),

their

_phases

_(information

about the formation

_history)

and their relaxation rates

_(incl.

chemical reaction

_rates).

_Essentially,

the

_technique

parallels

anidealFT-NMR

experiment,

whereonewould monitor the FID afteran

infinitely

_strong

90°-pulse.

Like

EPR,

_/zSR

is nota surface

specific technique.

The main obstacle

is,

ofcourse, to thermalize sufficient muons outside the bulk material. It

has been

_firmly

established

_that,

_by

_using

a 7nm diameter _non-porous

silica

_powder

as a

probe,

the muons almost

exclusively

thermalize as Mu inthe void

_regions

between the

_{powder grains [43].}

A

_negative

work func-tionmaybe

responsible

for thisobservation

[44]. Fig.

7shows the relaxation rate for Mu on a silica surface as a function of

_temperature

[45].

Below

Fig.6.Schematic of the time-differentialpSR experiment. S: sample, a,b,

c,f¡,f2,

Pi, p2:scintillation counters,D:degrader. :magneticfield.Reproducedfrom Ref. [41]with

permission

of the author.

20 10 5

Fig.7. Mu relaxationrateon asilica surface inatransverse

_magnetic

field of 7.3 10" •: Si02evacuatedat383K;

permission

of the author. Si02

evacuatedat873 K. Redrawn from Ref.[45]with

8

K,

Muis localizedonthe

surface,

the relaxationrate

_{being mainly}

caused

by dipolar

interactions with the surface

_hydroxyls.

Above 8

_K,

Mustarts to move on the surface and motional

narrowing

decreases the relaxation

rate,untilMu becomes localized in

_deeper

_traps

at25 K. From

longitudinal

1-1-1-1-;-1-1-1-1-1-1-1-

200 220 240 260 280 300 32C

FREQUENCY (MHZ!

Fig.8. Fourier _{power spectrum} of the muonated cyclohexadienyl radical on a fully

hydroxylatedSi02 surfaceatroom_temperatureinamagneticfield of0.238 T.

impurities (about

6

_ppm).

At still

_higher

_temperatures

_detrapping

and

eventually desorption

ofMuoccurs.

In addition to the reaction kinetics of Mu with

ethylene

on a silica

surface

_[46],

the reaction of Mu with a

platinum-loaded

silica surface has

been studied. The

_{Pt-crystallites}

werecovered

by

oxygenanda

_steep

increase

ofthe relaxation ratearound40—60 has been

_interpreted

in termsofa chemical reaction

_{[47, 48]:}

Mu +

_O(ads)

-» OMu

·

Recently,

we succeeded to observe a muonated radical on a surface

[49].

Using

a

hydroxylated

silica

surface,

which was covered

by

_appr. a

monolayer

of

_benzene,

we wereableto detect the

cyclohexadienyl

radical.

The Fourier powerspectrumis shown in

_Fig.

8. Like in ENDOR

spectro-scopy, two

_frequencies

are

observed,

and their sum

equals

the

hyperfme

coupling

constant

_µ.

A

_large

difference in the

_amplitudes

of the two

frequencies

is evident. Due to _{the finite lifetime of the Mu precursor}

(compared

to the Mu

_{precession frequency),}

the muons do not enter the

product

state

_(the

_radical)

_coherently.

The

_resulting

_{depolarization depends}

on themuon

precession frequencies

in the _{precursor, in the}

product

state

andontheformationrate

[50].

The

simplicity

of the

spectrum

is remarkable

and itshould be

_possible

to

_study

the behaviour of muonated radicals on surfaces. In order to measure the other nuclear

hyperfme couplings

one hasto resort tothe

_{recently proposed [51]}

and

_developed

_{[52, 53] technique}

ofAvoided Level

_Crossing

_/tSR

in

_{longitudinal magnetic}

fields.

Although

the

_{possibilities}

of

_//SR

in surface science are

quite

limited

today,

this situation will

_{certainly improve}

in the near

future,

when near

thermal µ+

-or Mu-beams become available. There is now considerable

effortatthe

_major

mesonfactories to constructsuch beam lines.

5.

_Comparison

Although

all three

_{techniques directly}

measureNMRtransition

frequencies

in

_paramagnetic

_systems,

several distinct differencesare

_apparent.

In disordered

_systems

a

lineshape analysis

is,

of course, most

_easily

performed

in t/SR. No instrumental

_{perturbations}

_{(e.g electromagnetic}

fields,

modulation effects

_etc.)

are

_present,

and,

inaddition all orientations of the

_paramagnetic

_species

contributeto the

_lineshape.

This is incontrast to the orientation

_selectivity

in ENDOR and ESEM due to the finite excitation of the EPR

spectrum.

InENDOR orientation

_dependent

transi-tion

_{probabilities}

arise via the rf-enhancement effect and orientation

de-pendent

relaxation

_pathways.

In ESEM it is the modulation effect itself which is

_strongly

orientation

_{dependent. E.g. neglecting}

_quadrupole

inter-actions,

the modulation effect vanishes in a

point-dipole

model for

B0

parallel

or

perpendicular

to the electron-nuclear axis.

Thus,

for

_weakly

interacting

nuclei often

_only

a

bell-shaped signal

is observed

[54, 55].

It is

_important

to note,that the

_techniques

monitor different

_regions

of the

_{spin density}

distribution. ESEM

_mainly

_operates

inthe low

_frequency

region.

The

_branching

of transitions condition and thefinite

_timing

resolu-tion

_imposes

an _{upper limit} of _{appr. 30 MHz. On the other}

hand,

it _is

difficult to obtain an _{ENDOR response from}

weakly interacting

_nuclei

with low

_gyromagnetic

ratios due to difficulties in

_saturating

the NMR transitions. Likewise it is difficult to measure weak nuclear

hyperfine

frequencies

in

_{/¿SR [53].}

_However,

the

_timing

resolutionis much better than in ESEM andmuon

hyperfine frequencies

of> 4GHz have been measured

[56].

Compared

toENDOR the

_advantages

of ESEMare:

(1)

the normalized

modulation

_amplitude

is

_solely

determined

_{by Spin-Hamilton}

_parameters,

including

the numberof

_interacting

nuclei.

₍₂₎

ESEM isnot

_necessarily

less sensitive than

EPR,

an ENDOR _responseis

commonly

one to two orders

of

_magnitude

weaker than the EPR

_signal

and

₍₃₎

ESEM doesnot

depend

on adelicate balance ofrelaxation mechanismsas ENDOR does.

Although

both,

ESEM and

_//SR,

aretime-domain

techniques, only ßSR

itself is

_already

a kinetic method. The

paramagnetic

species

are created

during

the

_experiment

and their fate is followed for the first few micro-seconds after their birth. Unlike

ESEM,

does not suffer from in-strumental deadtime

_problems.

The

_versatility

of

_pSR

is,

of_course, restrictedtothe

_study

ofmuonated

species.

Finally,

it

_might

be worthwhile to

mention,

that whereas

and ENDOR-measurements often

_require

low

_{temperatures,}

this isnotthe

casefor

µ8 .

Acknowledgements

ThanksareduetoProf. H. Fischer and Prof. G. Lehmann for their

continu-ous interest and

support.

Preprints

from Prof. L. Kevan and Drs. D. R.

Harshman,

R. F.Kiefland E.Roduner

_prior

to

_publication

are

appreciated.

I also wish to thank Dr. E.

Roduner,

who introduced me to the field of

µ$ ,

forvaluable discussions.

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