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Pulsed EPR techniquesBasic concepts
Pulsed EPR course material provided by Sabine Van DoorslaerPhysics Department, University of Antwerp
Etienne Goovaerts, Physics Department, University of Antwerp
Course at CAB, San Carlos de Bariloche, Argentina, 6/12/2012
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Relaxation mechanisms
We work on a macroscopic scale -> different electron spins form an “ensemble”
-> typically paramagnetic phase, ± dilute spin system
We measure not of a single spinbut the magnetization
i
iVμM 1
bs-big
pulse EPR methods
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In thermal equilibriumBoltzmann distribution
between spin statesM along z (if B0 is on) -> M0
0BMM
dtd
If M out of equilibriumWe get a precession of the magnetization
because of torque on each of the magnetic moments
Relaxation mechanisms
pulse EPR methods
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SITUATION 1
System returns to equilibrium -> characteristic time T1(spin-lattice or longitudinal relaxation time)
Mz= 0 Mz = -M0
Mz= M0(1-e-t/T1) Mz= M0(1-2e-t/T1)
Relaxation mechanisms
We bring magnetization out of equilibrium, such thatthe system is saturated (Mz = 0)
or the magnetization is inversed (Mz = -M0)
pulse EPR methods
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SITUATION 2
We turn the magnetization in the xy plane
Magnetization B0 -> rotation with Larmor frequency
At thermal equilibrium: magnetization in planeshould be 0 -> system will try to return to this situation
Mxy = Mxy,0 e-t/T2 Characteristic timeT2
Transversal or spin-spin relaxation
“pure” T2Molecular interactions
throughinhomogeneous field
1/T2* = 1/T2 + 1/T2,inhom
pulse EPR methods
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Combination of transversal and
longitudinal relaxation
pulse EPR methods
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Spin dynamics: classical pictureSpin dynamics: classical pictureSpin dynamics: classical picture
pulse EPR methods
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The ‘rotating frame’:
pulse EPR methods
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In the rotating frame:pulse EPR methods
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Pulsed microwaves:
pulse EPR methods
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Pulse EPR: FT EPRPulse EPR: FT EPRPulse EPR: FT EPR
Single pulse: free induction decay (FID)
pulse EPR methods
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Pulse EPR: FT EPRPulse EPR: FT EPRPulse EPR: FT EPR
pulse EPR methods
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Pulse EPR: need for echo detectionPulse EPR: need for echo detectionPulse EPR: need for echo detectionLine broadening + spectral hole burning
pulse EPR methods
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Pulse EPR: Electron Spin Echo (ESE)Pulse EPR: Electron Spin Echo (ESE)Pulse EPR: Electron Spin Echo (ESE)Primary (or Hahn) echo or 2-pulse ESE
pulse EPR methods
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Pulse EPR: ESEPulse EPR: ESEPulse EPR: ESEPhase cycling:
pulse EPR methods
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Pulse EPR: ESEPulse EPR: ESEPulse EPR: ESE
Multiple applications: relaxation times T1 , T2
resolution enhancement:– field-swept echo
– modulated echo: ESEEM:ESE envelope modulationnuclear hyperfine interactions
2D- spectroscopiescorrelation between nuclei
pulse EPR methods
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Measuring nuclear interactions ESEEMElectron spin echo envelope modulation
S=1/2 coupled to nuclear spin Iby hf interaction
Need for density matrix description(not fully developed here)
pulse EPR methods
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/2 pulse creates electron coherence= in-plane rotating electron magnetization
Specific vector contributions in 4x4 density matrix
/2)x
S=1/2, I=1/2
21
34
| ½ -½ >| ½ ½ >
| -½ ½ >
| -½ -½ >
ECa
ECf
What happens after a /2 pulse ?
x
z
y
x
z
y
M/2)x
x
z
y
Different rotation frequencies among spins?
ECa
pulse EPR methods
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In ESEEM, we use a series of microwave pulses
General outline of an ESEEM experiment
evolutionevolutionmixingpreparation detection
n
EC, NCEP, NP
ECEPNPECNC
EPNPECNC
detection of spin echo vs. inter-pulse distance
time domain frequency domainF.T.
pulse EPR methods
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Two-pulse ESEEMS=1/2, I=1/2
1 2
34
| ½ -½ > | ½ ½ >
| -½ ½ >| -½ -½ >
(1,3)
x
yx
z
y
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
1
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
2
x
y
(1,3)
After time magnetization has gained phase
S=1/2, I=1/2
S(1,3)=(13‐mw)
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
pulse inducesflip of magnetization but also
redistribution of electron coherence
x
y(1,3)
(2,3)(1,4)
(2,4)
S=1/2, I=1/2
3
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
x
y(1,3)
(2,3)(1,4)
(2,4)
3
1 2
34
| ½ -½ > | ½ ½ >
| -½ ½ >
| -½ -½ >
S=1/2, I=1/2
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
After time the magnetization M(i,j) have gained
a phase
(S(i,j) - S
(1,3)) = (ij – 13)
S=1/2, I=1/2
4
x
y(1,3)
(2,3)
(1,4) (2,4)
12
34 -
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
4
Example:(S
(1,4) - S(1,3)) = (14 – 13)= 34
1 2
34
| ½ -½ > | ½ ½ >
| -½ ½ >
| -½ -½ >
x
y(1,3)
(2,3)
(1,4) (2,4)
12
34 -
34
S=1/2, I=1/2
pulse EPR methods
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Two-pulse ESEEM
/2)x x
evolution
detectionpreparation mixing
EC EC EC EC
1 2 3 4
4
Example:(S
(1,4) - S(1,3)) = (14 – 13)= 34
x
y(1,3)
(2,3)
(1,4) (2,4)
12
34 -
S=1/2, I=1/2
Changing pulse interval
Echo modulates with nuclear frequencies !
pulse EPR methods
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�/2 �
� �
FTNZ
A
Q
Two-pulse ESEEMpulse EPR methods
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Two-pulse ESEEM
V2p() = 1 - (k/4)[2-2cos()-2cos()+cos()+cos()]
Modulation formula for an S=1/2, I=1/2 system
No ESEEM for isotropic hyperfine or hyperfine principal directions
-> no ESEEM for a molecule in a non-viscous solution at room temperature
(|12|=, |34|=)
pulse EPR methods
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Two-pulse ESEEM
Advantage of 2-pulse ESEEM
Very fast method
Drawbacks of 2-pulse ESEEM
1. Overlap of signals: one-dimensional technique + line broadening
2. Depends on electron spin-spin relaxation which is often very short, so that one has broad signals
pulse EPR methods
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/2 /2 /2
TEvolution time
3-pulse ESEEM sequence
Note : in three-pulse ESEEM no - and + are found !-> simpler spectrum than two-pulse ESEEM
For = 2n/(n = 0,1, ...) blind spots in spectrum
Eliminate this artefact with sum over - values(but more measurements needed!!)
pulse EPR methods
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Phase cycling is needed to remove unwanted echoes
(Measurement on ‐irradiated quartz (G. Jeschke))
pulses
detection
-yy-yy
x-xx-x
2
xx-x-x
3
xxxx
HE=Hahn echo or primary echoRE=refocused echoSE=stimulated echo
pulse EPR methods
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Advantage of 3-pulse ESEEM
1. only basic frequencies2. T1 dependence of signal -> narrower lines
ESEEM
3-pulse ESEEM sequence
2-pulse ESEEM
3-pulse ESEEM
Ferric cytoglobin
pulse EPR methods
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2D-ESEEM sequence: HYSCOREHyperfine sublevel correlation spectroscopy
1
2
F.T.
/2 /2 /2
t1 t2
t1t2
pulse EPR methods
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Pulse EPR: HYSCOREPulse EPR: HYSCOREPulse EPR: HYSCOREusing 4-pulse sequence:
pulse EPR methods
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Pulse EPR: 2D ESEEMPulse EPR: 2D ESEEMPulse EPR: 2D ESEEMpulse EPR methods
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Nanosecond mw pulses, kW amplificationfast spectroscopy (ns steps)
-> technically only possible from the 80s-> commercially available since early 90s
Relaxation times -> solids or frozen solutions
Pulsed EPR did not replace CW EPRNot possible to excite total spectrum
with one pulse
pulse EPR methods