Upali A Jayasooriya

School of Chemistry

University of East Anglia

Norwich, UK

*

Introduction

• Muon states in matter Implanted positive muons may exist in any of the following

forms.

a) Muon, μ+

b) Muonium, μ+e-

c) Part of a radical

• Properties of Muons?

Mass = 0.11 proton

Charge = +e

Spin = 1/2

Magnetic moment = 3.18 x proton

Larmor frequency = 13.55 kHz/G

Diamagnetic Muon States

Free muons ( +) Molecular ions (N2Mu+) Compound (MuOH)

It is not possible to distinguish between these states by measuring the

precession frequencies

O

Mu H

J

Maximum measuring time window ~ 32 microsec

Uncertainty principle . t ≥ 1/4 ~ 2.5 kHz

J ~ Hz

Properties of Muonium [ +e-]

Isotope Mass/me Reduced mass/me Bohr radius/nm Ionisation energy/eV

Tritium (3H) 5498 0.9998 0.05290 13.603

Deuterium (2H) 3675 0.9997 0.05293 13.602

Protium (1H) 1847 0.9995 0.05292 13.599

Muonium (Mu) 208 0.9952 0.05315 13.541

Paramagnetic muon states

Strength of interaction between the Muon Spin and the

Unpaired Electron Spin is given by the

Hyperfine Coupling Constant

Isotropic contribution transmitted through bonds and is a

measure of the unpaired electron spin density at the nucleus

20 06

XeX

hA

Anisotropic contribution is due to the magnetic dipole interaction

between the unpaired electron and the nucleus

32

1

4 r

hD Xe

X

Muon - Electron system; Breit - Rabi diagram

Singlet

Energy

Magnetic Field

Triplet

A 24

12

34

e- +

+ +

+ -

- -

- +

|3>

|2>

|4>

|1>

ms

+1

0

-1

0

Polarisation

Relaxation

LF

-time differential

Rotation

TF

ALC

LF

-time integral

• Validate

• Extend

•Novel applications

* Mig Roduner et al

•Reaction Kinetics

O

Diallylether

Mu

O

Mu •

O

Mu

•

Rates of Radical Cyclization

P. Burkhatd et. l. J. Phys.

Chem. 88 (1984) 773

k

TF-MuSR

k (338K) = 9.3 x 106 s-1

and compares well with

the literature estimates

of

k (338K) = 8.8 x 106 s-1

* Paul Percival et al

•Studies in supercritical liquids

*

0 100 200 300 400 500

Temperature /°C

0.0

2.0

4.0

6.0

8.0

k / 1

010 M

-1s

-1

M3

M1

AECL

M2

current PWR reactors

next generation reactors

Data limited to 200 C

Buxton and Elliot,

JCS Far. Trans. 89 (1993) 485

Ghandi and Percival, J. Phys. Chem. A 107 (2003) 3006

*

At 25 C the keto-enol equilibrium constant of acetone in water is

5 10-9

H C 2 M u

O

H

M u

O

M u

M u

H g e m e a t u e i h t p r r :

O

O H

Low temperature:

240

260

280

- 100 0 100 200 300 400

Temperature / °C

0

20

40

60

Muon h

yperf

ine c

onst

ant

/ M

Hz

C H 2 M u

O

H

O

M u

keto and enol forms of acetone give

“different” radicals

Ghandi, Addison-Jones, Brodovitch,

McCollum, McKenzie, and Percival,

JACS 125 (2003) 9594.

O

H

C H 3 C H 3

0.8 1.0 1.2 1.4 1.6 1.8 2.0

Field / kG

A+-A

-

(a)

9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8

Field / kG

A+-A

-

(b)

The Mu adducts are isomeric

radicals

C H 2 M u

O

H

C H 3

O

M u

C H 3 C H 3

92°C

136 bar

350°C

250 bar

Migg Roduner et al

• Guest molecule partitioning in soft matter structures

Guest molecule

[3-phenylpropan-1-ol]

Surfactant

[2,3-diheptadecyl

ester ethoxypropyl-

1,1,1-

trimethylammonium

chloride]

Radical located

within the bilayer*

Radical located

in aqueous layer

Molecular Dynamics

Theory

222

22

ωτ1

τ.

x1

x.A2π2.λ

ijij

2

ijij ω.φ.PMλ

Coupling of

perturbation Change in muon

polarisation Spectral density

of perturbation

S.F.J. Cox and D.S. Sivia, Hyperfine Interactions 87 (1994) 971

Organometallics

Metallocene ring dynamics at temperatures of relevance to „polymerisation catalysis‟ fall within the SR time window

H

Mu Fe

Mu

Fe

H

Mu

Fe

FERROCENE

Fe-Mu radical cp-Mu exo-radical

cp-Mu endo-radical

0 50 100 150 200 250 300 350 400 450

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Re

lax

ati

on

/

s-1

Temperature / K

0 50 100 150 200 250 300 350 400

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Re

lax

ati

on

/

s-1

Temperature / K

4 6 8

22

23

24

25

26

ln (

/ )

(1000 / T) / K -1

4 6 8 10 12 14 22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

26.0

ln (

1/ )

(1000 / T) / K -1

E = 3.4(0.4) kJ mol-1

E = 5.8(0.4) kJ mol-1

= 6.3(1.7)x1011 s-1

= 1.1(0.4)x1012 s-1

Cp-M

u r

epola

rise

s like b

enzene

Fe-M

u

e2u

e1g (xz,yz)

e2u

e1g

e1u

a1

u a1

g a1g

a1u

d(a1g,e1g,e2g)

e1g

e1u

e2g (x2-y

2,xy)

a1g (z2)

e2u

e1g (xz,yz)

e2u

e1g

e1u

a1u

a1g a1g

a1u

d(a1g,e1g,e2g)

e1g

e1u

e2g (x2-y

2,xy)

a1g (z2)

E = 5.8(0.4) kJ mol-1

= 1.1x1012(0.4) s-1

E = 3.4(0.4) kJ mol-1

= 6.3x1011(1.7) s-1

Agrees with NMR & QENS values

for cyclopentadienyl ring rotation

LUMO

LUMO

NON BONDING

ANTI BONDING

Photoelectron spectroscopic evidence to show the drop in energy

of the d-orbitals across the Periodic Table.

Evans et al, J.Chem.Soc., Farad. Trans II, 68 (1972) 249

Benzene chromium tricarbonyl

Cyclopentadienyl manganese tricarbonyl

LUMO non-bonding

LUMO anti-bonding

Agree with NMR values of

activation energy

Ruthenocene

Osmocene Do not agree with NMR values

Ferrocene Both types

Ferrocene encapsulated in KY-zeolite C.T. Kaiser et al Chem. Phys. Letts., 381 (2003) 292

• Muon spin relaxation shows only one radical species

On encapsulation in the zeolite: • Ferrocene becomes very reactive to air

• NMR and QENS show no change in ring rotation dynamics

• SR shows a significant hardening ( E = 9.7 kJ mol-1) of the ring rotation dynamics

These observations are compatible with the non-bonding orbital of ferrocene in the encapsulated state being the LUMO and is depressed in energy due to interaction with the zeolite cage.

This thus reduces the HOMO-LUMO gap thus affecting the chemical reactivity.

e2u

e1g (xz,yz)

e2u

e1g

e1u

a1

u a1

g a1g

a1u

d(a1g,e1g,e2g)

e1g

e1u

e2g (x2-y

2,xy)

a1g (z2)

e2u

e1g (xz,yz)

e2u

e1g

e1u

a1u

a1g a1g

a1u

d(a1g,e1g,e2g)

e1g

e1u

e2g (x2-y

2,xy)

a1g (z2)

NON BONDING

ANTI BONDING

a1g(z2)

Zeolite orbital

HOMO

LUMO

a1g(z2)

e2u Free Ferrocene

Encapsulated Ferrocene

* Interfacial Transfer

*Rapid Process

*– close to diffusion controlled?

*Available techniques?

*Rotating Diffusion Cell

*Stopped Flow

*Line Broadening Methods

* NMR

* ESR

* SR ???

* A : TF- SR

* An: M = 0, ALC

Oil

Water

XOIL

XWATER

* Probing Exchange Dynamics

*Two site exchange

*RMu●water RMu●

oil

k1

k-1

110 111 112 113 114 115 (MHz)

110 111 112 113 114 115 (MHz)

110 111 112 113 114 115 (MHz)

k < A k ≈ A k > A

* Rates from Linebroadening

•Analytical expression

•Lineshape simulations

–Ab initio methods

• QUANTUM (from James Lord)

–Monte – Carlo

• Roduner et al Chem. Phys. 203 (1996) 317-337

*

* Criteria for Line Broadening Approach

Probe Molecule

- Show balanced partitioning between O and W phases

- Stability

System

- Large interfacial area required

- Expect rapid exchange so high concentrations required to avoid

diffusion control

Spectroscopic Technique

- Provide suitable frequency window EXP ~ k

i.e. sensitivity to solvent environment for good separation between O

and W

* Criteria for Line Broadening Approach

Spectroscopic Technique - Muon Spin Spectroscopy SR

• Muoniated radicals exhibit high sensitivity to environment (solvent

polarity)

• Gives time (frequency) window EXP = MHz range

• Different peaks from muonated radicals may show variation in EXP (i.e. a

choice of time windows may be available)

• Wide choice of possible probe molecules (only unsaturation required)

*Avoided Level Crossing ALC- SR

Can get spin transitions at the

“level crossings” i.e.

depolarisation

At high field only -p proton

spin exchange occurs (flip-

flop)

Gives Ap

Energy of spin ( or ) states of electron

(e) muon ( ) and proton (p) in a

muoniated radical

*Principle of the experiment

Muoniated Allyl Alcohol (AA) Radical

(AA is CH2=CH-CH2-OH)

Water-in-oil

Microemulsion AA = 0.07

PW ~ 0.58 PO ~ 0.42

*ALC signals from Muoniated AA

4

6 possible ALC peaks

+e-

2 possible radicals

1

3

2

4

5

*ALC signals from Muoniated AA

Results for AA in Heptane

6 possible peaks - 5 observed

3 at “lower” field 2 at “higher” field

1.20 1.25 1.30 1.35 1.40

-0.010

-0.005

0.000

Po

lari

sa

tio

n

Field B / Tesla

1.85 1.90 1.95 2.00 2.05 2.10

-0.010

-0.005

0.000

Po

lari

sa

tio

n

Field B / Tesla

3 peaks (1,2 and 4) show good statistics

– suitable for broadening measurements

1 2

3

4

5

*Antioxidant Capacity

• There are a number of methods of quantifying ‘Antioxidant Capacity’

• No agreement between these methods

• Probe molecules used are of different sizes

J. Tabart, C. Kevers, J. Pincemail, J-O. Defraigne, J. Dommes, Food Chemistry, (2008)

• Muonium is the smallest radical species known and hence the steric requirements are negligible

• Rate of reaction/quenching of the muonium radical is measurable using very low field transverse field experiment.

• XkR0