Applications of mSR: Chemistry - isis.stfc.ac.uk
Transcript of Applications of mSR: Chemistry - isis.stfc.ac.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
O
Diallylether
Mu
O
Mu •
O
Mu
•
Rates of Radical Cyclization
P. Burkhatd et. l. J. Phys.
Chem. 88 (1984) 773
k
k (338K) = 9.3 x 106 s-1
and compares well with
the literature estimates
of
k (338K) = 8.8 x 106 s-1
*
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
Guest molecule
[3-phenylpropan-1-ol]
Surfactant
[2,3-diheptadecyl
ester ethoxypropyl-
1,1,1-
trimethylammonium
chloride]
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
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
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