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Catch Me If You Can! Studying Transient Radicals Using

Muon Spin Spectroscopy

Iain McKenzie

Centre for Molecular and Materials Science, TRIUMF, Vancouver, B.C. Canada and the Department

of Chemistry, Simon Fraser University, Burnaby, B.C. Canada

Most radicals, molecules containing unpaired electrons, are notoriously difficult

to study because their extreme reactivity typically results in a very short lifetime

but they are worth examining due to their ubiquity, often as intermediates in

chemical reactions. The muon spectroscopic techniques, commonly referred to

as μSR, are arguably the best tools we have for studying transient radicals in the

solid, liquid and gaseous states. In this talk I will show how μSR can be used to

determine the structure and dynamics of free radicals and present recent results

on organometallic radicals, strained organic radicals, spin probes in soft

condensed matter and the dynamics of radicals in solution.

Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada Propriété d’un consortium d’universités canadiennes, géré en co-entreprise à partir d’une contribution administrée par le Conseil national de recherches Canada

Canada’s national laboratory for particle and nuclear physics Laboratoire national canadien pour la recherche en physique nucléaire

et en physique des particules

Accelerating Science for Canada Un accélérateur de la démarche scientifique canadienne

Catch Me If You Can! Studying Transient

Radicals Using Muon Spin Spectroscopy

Iain McKenzie | CMMS | TRIUMF

Secondary*Adducts*

Ter0ary*Adduct*

•  Introduction •  Organometallic radicals •  Mu + [2.2]paracyclophane; strained organic

radicals •  Spin probes in soft matter •  Spin relaxation studies of organic radicals in

solution •  Electron hopping in Alq3?

A Hodgepodge of µSR Chemistry

September 12, 2012 Muoniated Radicals 2

The Muon, Muonium and Muoniated Radicals


µ+

e−

• Mµ = 1/9 Mp

•  Spin = ½ •  γµ = 3.183 γp •  τµ = 2.2 µs

B

µ+

• MMu = 1/9 MH

•  IPMu = 0.9956 IPH

•  Bohr radius = 1.0044a0

C CMu

H3CH

H3CH

Structure determined by measuring hyperfine coupling constants: Aµ, Ap

Mu

•  Through a better understanding of the behavior of the intermediates, we can better control chemical reactions

•  Radicals are often intermediates in chemical reactions, but….

•  Difficult to study with traditional spectroscopic techniques (EPR, UV-Vis, IR)

•  µSR is exceptionally sensitive for studying radicals in a wide range of environments

•  Determine how molecules react with a simple free radical

Why Study Muoniated Radicals?


€

reactants→ intermediate[ ] → products

Longitudinal Field Measurements


µ+!Sample

Forward Positron Detector

Backward Positron Detector

Spin-polarized muon beam

e+

B

Level Crossing Resonance


Ene

rgy

Pol

ariz

atio

n

Magnetic Field

αeβµβk

αeβµαk

αeαµβk

αeαµαk

muon-nucleus spin flip-flop ΔM = 0

muon spin flip ΔM = ±1

muon-nucleus spin flip-flip ΔM = ±2

BresΔ0 ≈

12Aµ − Akγµ −γ k

BresΔ0 ≈

Aµ2γµ

Organometallic Radicals


•  How does H/Mu react with ferrocene?

Fe Fe FeMuH

Mu

FeMu

H

Mu

endo exo

Cp Adducts 17 electrons

Ferrocene Fe Adduct 19 electrons

•  What are the structures of the resulting radicals?

ALC-µSR of Ferrocene


U. A. Jayasooriya et al., Chem. Eur. J. 2007, 13, 2266

•  Extremely confusing ALC-µSR spectra.

•  Many peaks (1.17, 1.19, 2.04, 2.44 and 3.26 T)?

•  Claimed that Fe and Cp adducts are formed.



0.5 1.0 1.5 2.0

-6

-4

-2

0

10 K 25 K 37 K 50 K 62 K 75 K

Cor

rect

ed In

tegr

al A

sym

met

ry /

%

Magnetic Field / T

2

3

4

5

6

7

8

0 20 40 60 80 100

230

235

240

245

250

0 20 40 60 80 1000.2

0.3

0.4

Am

plitu

de /

a.u.

(b)

(c)

|Aµ| /

MH

zTemperature / K

(a)

FWH

M /

T

Temperature / K

Aµ0 = 250.5(6) MHz

Aµ1 = 126(13) MHz

ΔE = 1.4(1) kJ mol-1

Δ1 Resonance

DFT Calculations of Mu Adducts of Ferrocene


UB3LYP/6-311++G(2d,p)

more stable by 72.5 kJ mol-1

Aµexo

20 MHz

Aµendo

-3 MHz

AµFe

-304 MHz

Muon dipolar tensor [155,-87,-68] MHz

Hypothesis: The radical does not adopt it’s minimum energy geometry due to interactions with neighbouring molecules.

A Compromise Solution?


Hypothesis: The radical does not adopt it’s minimum energy geometry due to interactions with neighbouring molecules.

A Compromise Solution?


Spin density distribution changes

Aµexo = 231 MHz; [14,-7,-7] MHz

Apendo = 45 MHz; [13,-9,-4] MHz



λe and λµ increasing with temperature Chemical reaction?

0 2 4 6 88

9

10

11

12

13

14

15

16

17

18

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Asy

mm

etry

/ %

Time / µs

10 K 37 K 50 K 75 K 100 K

(a) (b)

! µ / µs-1

Temperature / K

2

3

4

5

6

7

8

0 20 40 60 80 100

230

235

240

245

250

0 20 40 60 80 1000.2

0.3

0.4

Am

plitu

de /

a.u.

(b)

(c)

|Aµ| /

MH

z

Temperature / K

(a)

FWH

M /

T

Temperature / K

How Does Strain Affect Reactivity?


H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

Mu

Mu

H

H2C CH2

H2C CH2

H

Mu

Mu

[2.2]paracyclophane

exo endo bridge

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

Mu

Mu

H

H2C CH2

H2C CH2

H

Mu

Mu

12.6o

CH3H3C

tertiary secondary

Para-xylene

CH3

CH3

Mu

H

CH3

Mu CH3

Calculated Barriers for Addition


Site Barrier / kJ mol-1

Relative Yield /%

Exo 17.2 88

Endo 48.6 ~0

Bridge 20.4 12

Secondary 23.8 99

Tertiary 34.8 1

UB3LYP/6-311G(d,p)

Secondary 89.2 % Tertiary 10.8 %

ALC-µSR of Para-Xylene


1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

-2.0

-1.5

-1.0

-0.5

0.0

Cor

rect

ed A

sym

met

ry /

%Magnetic Field / T

1.6 1.8 2.0 2.2 2.4 2.6 2.8

-2.0

-1.5

-1.0

-0.5

0.0

Cor

rect

ed A

sym

met

ry /

%

Magnetic Field / T

Liquid Solid

Secondary ~60 % Tertiary ~40 %

ALC-µSR of [2.2]Paracyclophane


Δ1 Endo

Δ1 Bridge

Δ1 Exo

Exo Aµ = 530.9 MHz Δ1 = 1.95 T 67±1 % Endo Aµ = 169.9 MHz Δ1 = 0.62 T 22±1 % Bridge Aµ = 469.0 MHz Δ1 = 1.72 T 11±1 %

UB3LYP/6-311G(d,p)//UPBE0/EPR-II

0.6 0.8 1.4 1.6 1.8 2.0 2.2

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Cor

rect

ed A

sym

met

ry /

%

Magnetic Field / T

Steric interactions (separation ≤ 3 Å) raise the addition barriers at some sites.

Steric Interactions in the Solid State


Cholesterolic Liquid Crystal


O

H

H HO

Cholesteryl nonanoate

Aµ = 441.9 MHz Bres(Δ1) = 1.62 T

Ap = 120.4 MHz Bres(Δ0) = 1.72 T

UB3LYP/6-31G(d,p) //UPBE0/ EPR-II

1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80

Cor

rect

ed A

sym

met

ry

Magnetic Field / T

383 K

376 K

368 K

363 K

357 K

349 K

ALC-µSR of a Cholesterolic Liquid Crystal


Δ1 Δ0

40

60

80

100

350 355 360 365 370 375 380 38520

40

60

80

100

Δ1 F

WH

M /

mT

Δ0 F

WH

M /

mT

Temperature / K

N* I

Spin Label in the Chiral Nematic Phase


Wobbling around preferred axis

narrows Δ1 resonance

ϕc

1.3 1.4 1.5 1.6 1.7 1.8

0.7

0.8

0.9

1.0In

tegr

ated

Asy

mm

etry

Magnetic Field / T

Dµ

|| / MHz -10 -5 -2

Dµ|| = Dµ

|| cosφc + cos2φc

2!

"#

$

%&

FWHM ≈2 Dµ

||

3γµφ 2 ≈

kBTqcπ 2K

Amplitude of fluctuations determined

from Δ1 FWHM

350 355 360 3652.5

3.0

3.5

4.0

4.5

5.0

5.5

<θ2 >

/ rad

ians

2

Temperature / K

Spin Label in the Isotropic Phase


Slow isotropic reorientation narrows Δ1 resonance

1.3 1.4 1.5 1.6 1.7 1.8

0.6

0.8

1.0

Inte

grat

ed A

sym

met

ry

Magnetic Field / T

τR / µs

2 1 0.5 0.2 0.1 0.05 0.01 0.001

0.0 0.5 1.0 1.5 2.00

50

100

150

200

250

Δ1 F

WH

M /

mT

τR / µs

2.60 2.65 2.70

0.5

1.0

1.5

τ R / µs

1000/T / K-1

Rotational diffusion time determined from Δ1 FWHM

Spin Relaxation in a Radical with One I = ½ Nucleus


•  Relaxation due to transitions between 4 spin states.

•  Transition rates between the spin states given by relaxation matrix, R.

•  Simplified in zero magnetic field.

€

RAHF =

−18 6 12 06 −12 6 012 6 −18 00 0 0 0

#

$

% % % %

&

'

( ( ( (

1120

AX : AX[ ]τc

€

τc =4πr 3η3kBT

€

RSR =

−1 1/2 0 1/21/2 −3/2 1/2 1/20 1/2 −1 1/21/2 1/2 1/2 −3/2

#

$

% % % %

&

'

( ( ( (

⋅C 2 IkBT ⋅ τJ

€

τJ =I

8πr 3η

Modulation of Anisotropic Hfcc Spin-Rotation Interaction

M. V. Fedin, J. Chem. Phys. 2003, 118, 192

Spin Relaxation in a Radical with One I = ½ Nucleus


I. McKenzie, PCCP. 2011, 13, 1168

€

Pz t( ) = 2 ni t( ) i ˆ I zµ i

i=1

4

∑ = n1 t( ) − n3 t( )

€

n1 t( ) =14

+14exp −

Aµ : Aµ[ ]πr 3η3kBT

%

& ' '

(

) * * t

+ , -

. -

/ 0 -

1 -

n2 t( ) =14

n3 t( ) =14−14exp −

Aµ : Aµ[ ]πr 3η3kBT

%

& ' '

(

) * * t

+ , -

. -

/ 0 -

1 -

n4 t( ) =14

€

n1 t( ) =14

+14exp −

C 2 I 2kBT8πr 3η

%

& ' '

(

) * * t

+ , -

. -

/ 0 -

1 -

n2 t( ) =14

n3 t( ) =14−14exp −

C 2 I 2kBT8πr 3η

%

& ' '

(

) * * t

+ , -

. -

/ 0 -

1 -

n4 t( ) =14

Modulation of Anisotropic Hfcc Spin-Rotation Interaction

€

λ =Aµ : Aµ[ ]πr 3

3kB

$

% & &

'

( ) ) η

T

€

λ =C 2 I 2kB8πr 3

$

% & &

'

( ) ) Tη

Different dependence of λ on temperature

and viscosity.

•  No nuclei with I > 0 •  σ radical

Formation of a Radical with One I = ½ Nucleus


Most radicals have multiple nuclei with I > 0

Muoniated 1,2-Dicarboxyvinyl 1,2-Dicarboxyacetylene

C CC

C

O

O

O

O

MuMu

C C CC

O

OO

O

Radical contains no I > 0 nuclei apart from the muon

Identification of the Vinyl Radical


0 100 200 300 400

!µ

!12

!43

2.9 kG

!µ

Four

ier P

ower

Frequency / MHz

!12

14.5 kG

TF 2G

Aµ = 491.4 ± 0.2 MHz

Dominant relaxation mechanism is modulation of anisotropic hfcc by molecular rotation

Spin Relaxation in Zero Magnetic Field


0 2 4 6 8 10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Muo

n S

pin

Pol

aris

atio

n

Time / µs-1

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.20.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

! / µ

s-1

"T-1 / 10-6 kg m-1 s-1 K-1

a t( ) = aRe−λµt + aD λµ ∝η T

Spin Relaxation of the 2-Muoxy-Prop-2-yl Radical


H3CC

CH3

O

H3CC

CH3

OMuMu

1 10 100 10000.05

0.10

0.15

0.20

1/T 1µ

/ µs-1

Magnetic Field / G

1 10 100 1000

0.2

0.4

0.6

0.8

1.0

Polarization

Magnetic Field / G

λµ = λµ0 + A τ c

1+ωµ2τ c

2

Mu lifetime > 220 ps Aµ

radical = 53 ± 6 MHz

radical Mu τc = 4.17(2) ps

Spin Relaxation of the C6H6Mu Radical


Mu

H

Mu

100 10000

1

2

3

λ µ / µ

s-1

Field / G

λµ ∝1B

10 100 10000

5

10

15

20

25

Total Asymmetry Relaxing Component Non-relaxing component

Asy

m (%

)

Field (G)

Electron Transport in Alq3?


€

G t( ) = exp Γt( )erfc Γt( )

•  Assumed relaxation due to 1-D electron diffusion

•  Fit LF-µSR spectra with Risch-Kehr function

A. J. Drew et al., PRL 2008, 100, 116601

D = 1.4±0.2 x 1012 s-1

ψ2(r = 0) = 0

No ALC spectrum

Electron Transport in Alq3?


A. J. Drew et al., PRL 2008, 100, 116601

€

Γ =ωo4

8ωeD2

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

H-Alq3

Ene

rgy

/ eV

HOMO

LUMO

A7A5

A2A4

Alq3

A6

A3

DFT Calculations on Mu Adducts of Alq3


UB3LYP/6-31G(d,p) A2 A3

A4 A5

A6 A7

Actual Behaviour in Alq3


LUMO

HOMO

Energy

Alq3 Alq3 Alq3 Alq3

Mu-Alq3

ΔG0 = 4.2 - 5.5 eV λ = 0.3 - 0.5 eV

UB3LYP/6-31G(d,p)

ΔG0 = 4.3 - 5.7 eV λ = 0.2 - 0.5 eV

ALC-µSR of Alq3


Position Bres(�1)

/ T Bres(�0)

/ T

2 1.26 1.37

3 1.65 1.80

4 1.15 1.26

5 0.82 0.90

6 1.72 1.88

7 1.02 1.11

UB3LYP/6-31G(d,p)

L. Nuccio et al., Submitted to Nature Comm.

10 K300 K (b)

Gaq3

1.61.41.21.00.80.6Magnetic Field (T)

10 K300 K (d)

Biq3

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

Pola

risat

ion

1.61.41.21.00.80.6Magnetic Field (T)

10 K300 K (c)

Inq3

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65Po

laris

atio

n 10 K300 K (a)

Alq3

10 K300 K (b)

Gaq3

1.61.41.21.00.80.6Magnetic Field (T)

10 K300 K (d)

Biq3

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65Po

laris

atio

n

1.61.41.21.00.80.6Magnetic Field (T)

10 K300 K (c)

Inq3

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

Pola

risat

ion

10 K300 K (a)

Alq3

0.6 0.8 1.0 1.2 1.4 1.6

•  µSR is a powerful technique to produce and characterize short-lived organic and organometallic free radicals in the solid, liquid or gaseous states.

•  The muon is a local probe; you need to understand it’s local environment before you draw conclusions about material properties

Conclusion


Acknowledgments


• Robert Scheuermann • Alexey Stoykov • Kamil Sedlak

• Steve Cottrell • Sean Giblin • Adrian Hillier • Philip King • James Lord • Francis Pratt

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