Surface Dynamics of the Cyclohexadienyl Radical Adsorbed on Silica Gel Investigated Using Avoided Level-Crossing Muon Spin Resonance

Oldenbourg

Surface

_Dynamics

of

the

_{Cyclohexadienyl}

Radical

Adsorbed

on

Silica Gel

Investigated

Using

Avoided

_{Level-Crossing}

Muon

_Spin

Resonance

By

Martina

_Schwager,

Emil Roduner*

Physikalisch-Chemisches

Institut derUniversitätZürich, Winterthurerstrasse 190,CH-8057 Zürich, Switzerland Ivan D. Reid

Paul ScherrerInstitute,CH-5232VilligenPSI, Switzerland

Sydney

R. Kreitzman

TRIUMF,4004 Wesbrook Mall,Vancouver, BritishColumbia, Canada V6T 2A3 Paul W.

Percival,

Jean-Claude

Brodovitch,

_{Siu-Keung Leung}

and

_Sunny

Sun-Mack

ChemistryDepartment, Simon Fraser_{University, Burnaby,} BritishColumbia, CanadaV5A 1S6

Dedicatedto

_Professor

Dr.

_Harry

_Pfeifer

on_theoccasion

_of

_{his 65th}

_birthday

(Received

April

20, 1994)

Surface

diffusion

ISilicaI

_{Cyclohexadienyl}

radical I Muon

_spin

resonance

The

_dynamic

behaviour of the

_{cyclohexadienyl}

radicalon asilica surface has been

investi-gated using

the avoided

_{level-crossing}

muon

_spin

resonance

_technique.

Translational

mo-tion ofthe radical on a curved surface leads to

_partial

_averaging

of the muon-electron

hyperfine

anisotropy

and thustomotional

_narrowing

of the

_{experimental signal.}

A theo-retical model basedon astochasticLiouvilleformalism allows

interpretation

_{of the data}

in terms ofradical diffusion. Arrheniusbehaviourwith an activation energy of(10.8 ±

* _{To whom}

0.9)kJ/mol is observed. Specific deviations between theoreticalpredictions and experi-mental resultsindicate that thepotentialof thistechnique isnotyet

fully

exploitedand that the model canbe further refined.

Das

_dynamische

Verhalten des auf der Oberfläche von Silica adsorbierten

Cyclohexa-dienylradikals

wurde untersucht mittels

_{Avoided-Level-Crossing Myon-Spin-Resonanz.}

DieTranslation des Radikals auf dergekrümmtenOberfläche führtzueiner

Teilausmitte-lungder

_Anisotropie

der

_{Myon-Elektron-Hyperfeinwechselwirkung.}

Sie beeinflußt damit die Linienbreite deruntersuchten Resonanz. Diese wurde

_{interpretiert}

auf der Basis der stochastischen

_{Liouville-Gleichung}

für die Diffusion des Radikals, wobei Arrheniusver-haltenmit einer

_{Aktivierungsenergie}

von(10.8±0.9)kJ/mol

gefunden

wurde. Bestimmte

Abweichungenzwischen theoretischenVoraussagenund

_{experimentellen}

Resultaten zei-gen, daß das Potential derTechnik noch nicht

_{vollständig ausgeschöpft}

ist und daß das Modell nochverfeinertwerdenkann.

1. Introduction

The motion of molecules both on and off the surface is of fundamental

interest in

_heterogenous

_catalysis

since it determines theturnover

frequency

and the balance between unimolecular and bimolecular reactions. Nuclear

magnetic

resonance is well suitedto

study

the

_mobility

of adsorbed

diamag-netic

_molecules,

and

_pioneering

work concerned with the surface diffusion ofbenzene on silica

gel

was conducted in

Leipzig

[1—4]

and in Hannover

[5],

It was shown that intramolecular and intermolecular

dipolar

proton-proton

interactions between adsórbate

molecules,

and furthermore the inter-action with surface

_hydroxyl

_{groups and with}

_{paramagnetic impurities}

in the

adsorbent,

are

important

for the relaxation of the

_protons.

Relaxation

times were found to _{lie in the range of 1}

—

1000 ms

depending

on surface

coverage and on the

degree

of deuteration of adsórbate and surface

[3, 4].

Further studies of the surface

_mobility

of benzene were undertaken for an

A1203 [6, 7]

and a

graphite

[8]

surface.

Free radicals ate

potential

transient intermediates of

heterogeneously

catalysed

processes. Their surface

dynamics

is

just

as essential to _the

per-formance ofa

catalytic

_process asis the

dynamics

of

diamagnetic

reactants and

_products.

Due to _{the open shell electronic character and the modified} structure and

_energetics

of the molecular

orbitals,

the interaction of the

radical with the surfacecan be

expected

todiffer

_considerably

from that of the

_parent

_diamagnetic

molecule from which it was derived. On the other

hand,

the radical and its

_parent

should behave

_similarly

if the surface inter-action is dominated

_by

van der Waals forces.

Radicals are less

easily

amenable to studies of their surface

_dynamics

than are

diamagnetic

molecules,

since as soon as

they

are mobile

they

un-dergo

termination

reactions,

so that at

_{catalytically}

relevant

_temperatures

their concentration is

_usually

belowthe detection limitofmostconventional

experimental techniques. Recently,

a new

technique

which uses

positive

muons substituted as

polarised spin

labels in

organic

radicals has been

de-veloped

[9].

Themuons,obtained fromabeam line ofasuitable

accelerator,

are

stopped

in the

sample

and

incorporated

in the radical

by

addition of

muoniumatoms

_(Mu

=

µ+ß~

is

chemically

_a

light isotope

of

hydrogen

with one-ninth the mass of

H)

across unsaturated bonds. The time evolution of muon

spin polarisation

_{is the}

analogue

_ofa free induction

decay

in

pulsed

magnetic

resonance

[10].

It carries information about the

magnetic

interac-tion of the muon with the electron and with nuclear

spins.

Details of the

experimental technique

have been

_given

elsewhere

_[9,

_11].

The extreme

sensitivity

allows the detection of radicals at concentrations down to a

single species

in the entire

_sample.

It therefore

_permits

the

_{investigation}

of radicals adsorbed on surfaces under conditions where

they

show trans-lational

_mobility.

The

_dynamics

is deduced from the

_{partial averaging}

of the muon-electron

_{hyperfine anisotropy.}

This was demonstrated for the Mu

adductto

2,3-dimethyl-l,3-butadiene,

for which reorientational correlation

times wereobtained in the motional

narrowing regime

[12].

Observation

_using

the transverse field

_technique

is limited

_by

the

re-quirements

that radicals are formed within 10"9 _s,in order toavoid loss of

phase

coherence of the muon

spin,

and

by

the restriction that there is no

morethan one muon

present

in the

sample

at_{any time. An alternative}

tech-nique,

avoided

_{level-crossing}

muon

spin

resonance

(ALC-//SR)

in

longi-tudinal

_magnetic

fields,

allows the detection ofradicals evenwhen

they

are

formed over

periods

of the order ofa

microsecond,

provided

that the

tran-sition rate is

high enough

to

produce

a

siginificant

ALC

signal during

the muon lifetime

[13].

It is a

time-integral

technique

which can use the full

muon flux of the accelerator since there is noconstraint on the number of muons within the

sample

at _any

_given

time. Even under these conditions the concentrationof radicals is

_extremely

_low,

and bimolecular termination reactions are

negligible.

It was therefore

possible

using

this

technique

to observe

_{cyclohexadienyl}

and

_ethyl

radicals adsorbed on silica

[14-16].

Overmostof the

_region

ofa

_strong

external

magnetic

field,

eigenstates

ofa

3-spin

_system

(µ+,

_e~, andnucleus

p+

are all

spin-V2 particles)

are_pure

Zeeman states. Muons

_injected

with their

_spins

_parallel

or

antiparallel

to

this fieldarethus in an

eigenstate.

There is notime evolution and henceno muon

depolarisation.

The behaviour is different in the

region

ofanavoided

crossing,

where the

_eigenstates

are mixtures of two Zeeman states. This leads to an oscillation between the two states, and if

_they

differ in the

z-component

of the muon

spin,

to a decrease in

polarisation.

It is detected as a resonance in a

plot

of the muon

_asymmetry

against

field

strength,

which is

_{given by}

the normalised difference of the

_positron

counts in two sets of detectors

_placed

in the forward and backward directions relative to the initial muon

spin

[13].

There are different ALC transitions classified

according

to the

_change

in the total

_spin

_quantum

number M of the

_{participating}

Zeeman states

_[14].

The resonance

obeying

the selection rule M =

0,

essentially

_a

muon-proton

spin flip-flop,

occurs under

isotropie

conditions to the first orderat

a resonancefield

A„-A„

A„

+

_A.

7m~ 7

(1)

where

_{Atn Ap}

are the

isotropie hyperfine coupling

constantsof themuon and

the

nucleus,

and yf„ yp their

gyromagnetic

ratios. This transition is driven

by

the

_isotropie

as well as the

anisotropie

interaction. In

isotropie

_systems

such as

liquids,

only

this

_type

of resonance is observed.

Increasing

ani-sotropy

of the

_system

broadens the

_signal

until it reaches a static line

shape

which

_is,

in

_general,

_asymmetric

fora

powder,

having equal

probability

for

all radical orientations.

A second

_type

of transition

_obeys

the selection rule

\A M\

= _{1. It}

corre-sponds

toa muon

spin flip

and occurs around

Br

=

-2

_1y„

_ye

(2)

It is driven

_by

the

_{anisotropie coupling}

elements of the Hamiltonian

_[17],

and therefore vanishes when the

_system

reorients onatime scale faster than

the inverse

_{hyperfine anisotropy.}

The resonance is thus absent under

iso-tropie

conditions but very

prominent

in solids

[18],

and it is

_expected

tobe

a sensitive indicator of small

anisotropies.

A

_strong

transition

_obeying

the selection rule A M = ₀

wasdetected for

muonated

_{cyclohexadienyl}

and

_{methoxycyclohexadienyl}

radicals adsorbed

on

_quartz

powders

[15].

It was observed that the resonance broadens with

decreasing

temperature,

and this was ascribed to slower reorientation of the radical. A reorientational correlation time was _estimated on the basis of a

jump

model.

Since

then,

the theoretical model has been

_greatly

_improved.

This work

provides

the first

_example

where the

_analysis

of

_experimental

data is based

on a stochastic Liouville formalism which was

adapted by

Kreitzman

[19]

to describe the

dynamics

at avoided level

_crossings.

It treats the effects of translational diffusion on a

spherical

surface,

electron

spin exchange

and

chemical

reaction,

andittakesintoaccount interactionbetweenresonances.

The

_system

under

_{investigation}

is the muonated

_{cyclohexadienyl}

_radical,

C6H6Mu,

adsorbed on the surface of silica

gel.

It differs from the

diamag-netic benzene molecule

_{only by}

_{the presence of the Mu} atom and should

thereforehave

_closely

thesamevander Waals interaction. Since the

adsorb-ent is also a silica

gel,

as in the

early

work on benzene

by

the

Leipzig

group, this should allow a

comparison

between the surface

mobility

of a

diamagnetic

molecule anda closeto related radical. In the

_latter,

the

650

_stronger

than that of the

_proton.

_{This has the consequence that the} nuclear relaxation rates increase

by

a

_large

_{factor. All}

_{proton-proton}

_dipolar

interactions are now

negligible,

instead,

the

dipolar

_part of the electron

nuclear

_{hyperfine coupling}

isthe relevant interaction that causesrelaxation.

Depending

onthedistance ofthe_{proton from the radicalcentre, the}

hyper-fine

_anisotropy

_may amount toas much as 30 MHz

[20].

The

experimental

time scale of

_dynamic

_{processes which}

_partly

_average outthe

_dipolar

inter-actions are thus

typically

a few tens of

_nanoseconds,

which is the same

order of

_magnitude

as correlation times amenable to the

_study

of

diamag-netic molecules

_by

means of NMR

[3].

For benzene adsorbed on silica

gel

it was

proposed by

Michel

[3]

that

the adsorbed molecules

_undergo

fast rotation about the sixfold axis down to

_temperatures

ofat least 130 K. This was _necessary to

_explain

the

tem-perature

dependence

of the _{intramolecular part} of the

_{proton ,}

relaxation data. It was

supported

further

by

2H NMR results of

benzene-<i6

adsorbed on

graphite

[8]

andonalumina

[6],

which demonstrated the

dynamic

behav-iour and the axial

_symmetry

downto low

_temperature.

The

_{cyclohexadienyl}

radical is also flat and

_rigid,

and it is

_plausible

that in a

monolayer

of

benzeneon silica its behaviour is the same as that ofbenzene. Its energy is

lowest when ituses the maximum

possible

contact area. Itis therefore

as-sumed to lie flaton the surface andto rotate

rapidly

_{about the axis}

perpen-dicular to the molecular

_plane,

_leading

to an

anisotropie

_system

of axial

symmetry.

Additional motion

_by

translation around the

_grains

orinside the

pores leads to an

averaging

of the axial

anisotropy

and renders the

_system

isotropie.

2.

_Experimental

A stainless steel sample cell with a window of 25_µ thickness was füled with 3 g of

silica gel (Aldrich Chemical Company, Inc.) which hada

_particle

size of 5 —

25_{µ ,}a

BET surface areaof 500

m2/g,

a_{pore volume of 0.75}

_cm3/g,

an_{average pore diameter}

of 6.0nm, and

ferromagnetic impurities

of 10 ppm.Itwas heatedat383 for24 hours undervacuum until a _{pressure of less than 10"5 mbar}was reached. This treatment

re-moves physisorbedwaterand leaves behindafully hydroxylatedsurface.

Benzene was

_degassed

with three _{freeze-pump-thaw cycles,}then adsorbed onto the silicagel to_givea nominal monolayer, assumingamolecularcrosssection of 0.40 nm2

[21].The isosteric heat of

_adsorption

of benzeneon a

_hydroxylated

silica surfaceamounts toca. 43 kJ/mol [22].The heat of

vaporisation

of

liquid

benzeneatroom_temperatureis

only

34 kJ/mol. This makessurethatC6H6condensesand

_spreads

onthesurface and that

it does notform

_droplets

or_{escape into the gas}

_phase

toa

significant

extent at room

temperature.

The ALC

_experiments

were

_{performed using}

a surface muonbeam at TRIUMF in Vancouver. The

_experimental

_setup and

_techniques

have beendescribed elsewhere [23].

The

_{applied magnetic}

fieldwasmodulated

nearly rectangularly by

nominally

±9.75mT,

I

ß

1.8 2.0 2.2

[Tesla]

Fig.

1.Raw

_ALC-¿fSR

spectrumof differentialasymmetry (arbitrary units)

against

longi-tudinal

_magnetic

field,takenat295 _(upper), with thefitted background,andat 193

(lower)with thesame background.

figurestoenhance thevisibility of thesignals by removing the

_sloping

baseline. For the analysis, the theoretical fit function was convoluted with the response function of the

magneticfieldto accountfortheexact_experimentalconditions.

3. Results and discussion

For the

_{cyclohexadienyl}

radical we

_expect

_{to find four ALC resonances}

corresponding

tothe selection rule AM =

0,

which involve the

méthylène

proton

(at

around 2.1

_T)

and the

ortho,

meta, and para

protons

(between

2.7 and 3.0

_T),

and the

_{\A M\}

= 1 _resonance around 1.9 T.

Figure

1

displays

the raw

_spectrum

obtained in the range of 1.55-2.25 for two

temperatures.

A

_sharp

resonance is

clearly

observed at 2.1 T. Two further

lines were seen at 2.904 and at 2.964

(ortho

and para

protons).

They

clearly identify

the

radical,

but

_they

were too weak for

_quantitative

work andarethereforenot used. At 295 thereseemstobeasmooth

background

(solid line)

with no indication ofa

\A M\

= 1 line. At 193

K,

however,

a

clear but broad feature is observed around 1.9 T. In order to follow the

spectral changes

with

_temperature

the identical

_{experimental background}

as

1. 1.8 2.0 2.2 1.6 1.8 2.0 2.2

[Teala] [Tesla]

Fig.

2.a)ALC-//SRspectraobtained with anominal monolayerof benzene adsorbedon

silica gel at varioustemperatures. The differential _asymmetry, with the

_background

of

Fig.

1 subtracted,is

_displayed.

The

_prominent

resonanceatound 2.1 Tesla is the M=

0 muon-proton spin

flip-flop

transition of the Mu, and the H bound in the méthylène position of the

_{cyclohexadienyl}

radical. The weak feature around 1.94 Tesla is the

\ M\

= _{1 muon}

spin flip

resonance, b) Fit of the M = 0 _resonance with _a model

consideringsmallanglerotationaldiffusion,and simulation of the lower field

_region

with the derived fitparameters.

Figure

2a showsaselection of

typical

_spectra

takenatdifferent

tempera-tures in therange of 132—295 K. Around 2.1 Tesla the M = 0

transition,

due to the

_méthylène

_proton

_coupling,

is observed

_clearly

down to 169 K. With

_decreasing

_temperature

a

broadening together

with loss of

intensity

occurs, and at 132 this

_signal

is no

longer

observable. At 234 a weak

\A M\

= 1 transition appears,

becoming

stronger

at lower

_temperature,

with

a maximum relative

intensity

around 193 K. Its

position,

which is

directly

proportional

tothe muon

spin coupling, Eqn

(2),

shifts to

_higher

fields with

decreasing

temperature.

The

_region

of the M = 0 transition _was

analysed

in _terms of the theoretical modelofsmall

_angle

rotational diffusion of the

_{cyclohexadienyl}

radical. The

_fitting

function is available in numerical form

_only.

_The param-eters are the

isotropie hyperfine couplings,

µ

and

Ap,

their axial

Table 1. Results of least squares analysis forthe isotropie hyperfine couplingconstants

of the muon(A„),theméthylèneproton (Ap),the rotational diffusion coefficient Dra,the

experimental

scale factorS, andthe

_{background given by}

a + b (B-Br).

[ ] A " [MHz] [MHz] [MHz] a [KT4] b [ "1] 295 275 255 234 213 193 169 516.43 517.93 519.34 520.91 522.48 524.05 525.85 126.41 126.48 126.49 126.52 126.77 126.96 127.83 13.9(4) 9.9(3) 6.3(2) 3.8(1) 2.7(1) 1.6(1) 1.1(2) 0.133(1) 0.110(1) 0.088(1) 0.0691(8) 0.0518(8) 0.0309(8) 0.0158(7) -0.6(4) 2.8(5) 8.3(4) 13.2(4) 17.8(4) 22.2(4) 26.2(3) 0.014(1) 0.019(1) 0.0138(7) 0.0111(5) 0.0094(4) 0.0103(5) 0.0031(4) *

Parameterfixedinthe fit.

was called vrin

[19])

for

isotropie

rotational diffusion

by

translation of the radical on the outer or inner surface of a

sphere

of radius

R,

the

signal

amplitude

S,

which is

_proportional

tothe radical

_yield,

anda

sloping

back-ground.

Of

_these,

_only

_Ap,

_DrM,

S,

and the

_background

_parameters

were

treated as variables.

They

are listed in Table 1. The

anisotropie

hyperfine

parameters

were_taken asconstant. An electron relaxationrateof 0.25 MHz

as determined for the

liquid by

Heming

etal.

[24]

was usedatall

tempera-tures, but it has no

significant

effect on the results. This rate is not

_strictly

temperature

independent

and has a maximum for € =

1,

which is the

casewhen is of the order ofa few

picoseconds

atthe

_magnetic

field used here. It is not

_expected

that our _systems are on the fast side of this

maxi-mum, sothatlower

_temperatures

have a lowerrelaxation rate, and theroom

temperature

value usedhere

_represents

the maximumtobe

_expected

inour

temperature

range. Basedonthe

experience

of

experiments

with bulk

liquid

benzene,

chemical reaction was

neglected.

Over the entire

_temperature

range, the

_positions

of the

_{|zl M\}

= 0

reso-nances are shifted to

_higher

fields

_by

ca. 9.2 mT

compared

with those in

bulk

_liquid

benzene at the same

_temperature

[25],

which is in

_agreement

with

_previous

observations

[15]. B,

depends

on the difference

Af—Ap

Eqn. (1)

and,

since the two nuclei

participating

in the resonance are

chemi-cally equivalent,

it is assumed that both

_coupling

constants _contribute

pro-portionally

to this shift and that an identical resonance

position

re-presents

identical values of

_µ

and

_Ap.

On this

basis,

_{µ( )}

was estimated

from its value at 295

(taken

from the

_liquid

at the

_temperature

with identical

_Br)

and its

_temperature

_dependence

on the

Si02 surface,

dA/dT

=

—0.075(6)

MHz/K,

and used as a non-variable

_parameter.

µ

is thus

slightly

higher

on a silica surface thanin the bulk

liquid

at the same

tem-perature,

as has been noted

previously

[15].

It is consistent with the above

Ap

ofthe

_méthylène

_proton

_(Table

₁₎

are also

larger

for the adsorbed case

compared

with the

_liquid

[25],

and that

_they

exhibit a similar

_temperature

dependence.

The error in

µ

is estimated to be

^0.5%,

which can affect

DTOt

by

as_much as 5%.

£y±

for the muonium-substituted

_{cyclohexadienyl}

radical was estimated on the basis of the tensor measured for the

_{corresponding}

Mu adduct to

durene

_[26].

It was scaled

by

the ratio of the

isotropie coupling

constants of the two

radicals,

and then the

_dynamic

_average was taken for fast rota-tion about the axis

_{perpendicular}

to the molecular

_{plane, leading}

to

_Z>[

= 3.18 MHz. The

_{corresponding}

_proton

_anisotropy,

Ty±

= 1.00

MHz,

was

estimated

_{by multiplication}

of the muon

hyperfine

value with the ratio of

magnetic

moments,

_{/ µ}

= 0.3141. These

parameters

influence

Drot

ap-proximately according

to

_(Z>[-Z>1)2,

so that an

uncertainty

of 0.1 MHz in

£>l-affects

the diffusion coefficient

_by

6%. The result of the fit over the AM = 0

resonance and its

extrapolation

tolower fields is shown in

_Fig.

2 b. The model works well for the A M = 0 transition at

_higher

_{temperatures,}

but below 240 it deviates

_{significantly.}

Whereas the

_experimental

A M = 0 line is of Lorentzian

shape

atall

tem-peratures,

the

_shape

of the fit function becomes

_{increasingly asymmetric.}

The theoretical

_prediction

deviates from the

_experimental

_spectrum

also in the

_region

of the

\A M\

= 1

resonance,and in

Figure

2b the

discrepancy

becomes most severe for the 255

_spectrum.

While a

pronounced

feature

is

_{predicted, only}

a weak

signal

is seen in the

experimental

data. At lower

temperatures,

the resonance is indeed

_present

in the

experiment

but

_always

broader than

_predicted.

It is

_generally

not

possible

toobtain aconsistent fit

overthe entire field range. In the fit overthe restricted range the mismatch

is accommodated in the

_temperature

_dependence

of the

_background

(coef-ficients a and b in Table

1).

Since the resonanceis the most

prominent

one

in solid benzene

_{[18, 15],}

its nearabsence for surface adsorbed benzene is

judged

to be _very

significant

and

obviously

of

_{dynamic origin.}

The exact

physical

process which causes the line tobe so weak is unclearat

_present.

Quantitative

analysis

therefore had to

_rely

on the M = 0 line alone. The orientational

_dynamics

of the

_hyperfine

tensor are reflected in the

rotational diffusion coefficients.Forthe _{surface adsorbed radical the}

averag-ing

over all orientations

depends

on the

grain

and pore size as well as on

its

_{shape, whereby}

smaller diameters lead to faster rotational diffusion. An Arrhenius

_plot

of the rotational diffusion coefficients is shown in

_Figure

3. The

_slightly

curved

_plot

is

_{approximately represented by}

the

_equation

Drot

=

(1.1

±

°oi)X

109s-1 ·

exp(-1300

±

100)

KVT.

(3)

The activation energy of

(10.8

±

_0.9)

kl/mol is similar to values for the difiusion of the benzene molecule on

hydroxylated

_porous

A1203

_(11.5

kJ/

mol

_[7])

andonsilica

gel

HR

(10.5

kl/mol

[4]).

Although

both thesubstrate

acti-1000

_K/T

Fig.

3.Arrheniusplotof therotational diffusion coefficient of the

_{cyclohexadienyl}

rad-ical,arisingfrom translational diffusionon a sphericalsurface.

vation

_energies

is

_{striking. Obviously,}

the radical and its

_parent

molecule have the same activation energy for diffusion on a

hydroxylated

surface,

and,

quite unexpectedly,

it does not seem to be of

_{primary importance}

whether this is on a surface of

A1203

or of silica. Ifthis coincidence is not

just by

chance,

then it would

_imply

that the

_binding

of the radical to the surface is dominated

_by

van der Waals forces and that the open shell

elec-tronic structure

_plays

a minor role. It would also mean _{that the interaction}

is

_mainly

with the surface

_hydroxyl

groupswhich mask the different nature

of the

_underlying

substrates. A final

_{interpretation}

can

certainly

not be drawn at this

_{point, especially}

since the extent of surface

_{hydroxylation}

depends

critically

onthe conditions of adsorbent

_pretreatment

[1].

The

early

NMR _{work used up} to 300

higher

_temperatures

in

_heating

out the silica

gel

before

_adsorption

of the benzene

[2—5].

This

_point

will be further ad-dressed in

_forthcoming

work

[21].

Small

_angle

rotational diffusion on the surface of a

sphere

with radius

R is

_equivalent

to two-dimensional translational diffusion onthe same

sur-face which for small

_angles

is

_{approximately planar.}

The two diffusion

equations

can be interconverted

using

the substitution =

r/R,

where is the rotation

_angle

and r the

magnitude

of the

displacement

vector on the

surface. This leads to

_Dtrans

=

R2Drot [28].

It

gives

_a

prefactor

of

D£ai»

= 1X10 8 _m2/s

for translational surface diffusion. Due to the

_irregular

_shape

of the pores

[29],

and since the molecule could in

_part

also roll instead of

just

slide on the

surface,

this is considered to be

_only

a

rough

estimate. It

is

_expected

to be affected

_by

features ofthe transition state of

_diffusion,

e._g.

by

radical-surfacevibrational

modes,

and

by

the average

jump

distance

and with

_neighbouring

molecules

[30].

At 298 we obtain

Dtrans

= 1.3

X10~10 m2/s. The

_{corresponding}

value in three dimensions amounts to

Aram

= 2.0 X10"10

m2/s,

which is

only

a factor of 11 below the value for

diffusion of benzene in the bulk

_liquid

at the same

_temperature

[31].

The

Arrhenius

_prefactor

will be further discussed in

_upcoming

work

[27].

The number of sites within reach for the

_diffusing

adsorbed

_species

depends

on its

root-mean-square

displacement

on the surface. This is in

general

also

_temperature

_dependent

and can cause a

prefactor

which

in-creases with

_temperature.

The curvaturein the Arrhenius

plot

(Fig.

3)

_may have tobe ascribed to this effect. A further

possible origin

is the

neglect

of

the

_{inhomogeneity}

of the surface: Different surface sites lead to a

distri-bution of

_isotropie

muon and

_proton

couplings.

This causes an

inhomo-geneous line

broadening

which is also

averaged

out asthe

species

becomes more mobile. The effectwould

explain

why

under near-static conditions at

low

_temperatures

the theoretical linecannot account for the full

experimen-tal width.

It is evident from Table 1 that the

_{signal amplitude}

also shows a clear

trend with

_temperature.

Under the conditions of our

experiments

5(7)

is

proportional

to the radical

yield.

Interestingly,

it shows a

good

Arrhenius

behaviour,

and its activation energy of 6.8 kl/mol is within error the same as that of the Mu addition reaction to _{benzene in the gas}

phase

[32].

It is

unlikely

that this isa _pure

coincidence,

rather it couldbe taken asevidence

that the activated reaction of radical formation

_competes

for Mu with

an-other,

unspecified

reaction offirst or

pseudo-first

order

kinetics,

so that the

radical is

_simply

not formed at low

_{temperatures.}

In

_agreement

with this

interpretation

is the fact that radicals formed on silica

by

Mu addition to

dienes,

which is much less activated

[32],

are observed down to far lower

temperatures.

Further measurements with benzene on _non-porous

spherical

silica

grains

of narrow size distribution are

being

written _up

[27].

They

include

measurements _{of the coverage}

_dependence,

and

_exploit

also

_platinum

and

palladium

loaded

material,

i. e. real

catalysts.

The _systems are more

accu-rate

_{representations}

of the

_present

theoretical model and are thus

expected

toallow a more detailed

interpretation.

Acknowledgments

Financial

_support

_by

the Swiss National Science Foundation and the Natural Sciences and

_Engineering

Research Council of Canada is

_gratefully

acknowledged.

TRIUMF is funded

_through

the National Research Council of Canada.

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