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Parahydrogen induced Parahydrogen induced polarizationpolarization

Thomas TheisUniversity of California Berkeley

Physics 250 04/17/2008

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The para-hydrogen The para-hydrogen phenomenonphenomenonUsed to create large polarization

from large population differences 10.000 fold NMR signal

enhancementHigh polarization can be exploited in

numerous applications◦ Detection of reaction intermediate

(especially in hydrogenations)◦ Characterization of gas flows (e.g. micro

engines, catalyst beds)◦ Characterization of fuel cells

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OutlineOutlineProduction of para-H2 Density Matrix descriptionPasadena vs. AltadenaFocus on basics rather than

applicationsovercoming hydrogenationsReference: Clifford R. Bowers, Sensitivity Enhancement Utilizing

Parahydrogen, Encyclopedia of Nuclear Magnetic Resonance

2002,9, 750-770.

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Dihydrogen wavefunctionsDihydrogen wavefunctionsNuclear wavefunctions:

symmetric

antisymmetric

total = e r n has to be symmetric (aacording to Dima, antisymmetric according to the literature)

ortho states live in the odd rotational states para state lives in the even rotational states (including J=0)

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Production of non-Production of non-equilibrium ortho/para equilibrium ortho/para hydrogen mixtures hydrogen mixtures Transitions between ortho and para hydrogen

are symetrically forbidden (para singletortho triplet)

non-equilibrium mixtures are long livedTo induce the transition catalysts at low temperatures break the symmetryOnce the hydrogen desorbs from the catalyst the

ortho/para ratio is conserved and given by

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Para-hydrogen enrichment

Percentage composition of ortho and para hydrogen as function of temperature

51% para @ 77K

99.9% para @ 4K

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Pairwise Hydrogenation using a catalyst e.g. Wilkinsons catalyst

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Pasadena

Parahydrogen and Synthesis Allow Dramatically enhanceed Nuclear allignment.

First published in 1986 from Bowers and Weitekamp at Caltech in Pasadena

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Direct product space reminder

z1 z2 z1 z2

z1 z1

1

1 1 0

0 0 0

0

1 0 0 0

1 0 1 0 0 1 0 01 1 1ˆ ˆ ˆ ˆ0 1 0 1 0 0 1 02 2 4

0 0 0 1

1 0 0 0

1 0 1 0 0 1 0 01 1ˆ ˆ E0 1 0 1 0 0 1 02 4

0 0 0 1

I I I I

I I

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General Hamiltonian for two General Hamiltonian for two spin systems and it’s spin systems and it’s EigenstatesEigenstates

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2 cos( / 2) sin( / 2)

3 sin( / 2) cos( / 2)

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z1 z1 z2 z2 1 2 z1 z2 1 2ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆH D[ 3 ] J I I I II I I I

tan( ) (D J) /

Rotating field Hamiltonian:

Eigenstates:

ωz1, ωz2: rotating frame chemical shiftsD: dipolar coupling constantJ: scalar coupling constant

Weak coupling limit: J,D 0

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Transition probabilitiesTransition probabilities2

p fi f i

1

2

3

4

1p 1 0

21 1

p 2 (1 sin )2 21 1

p 3 (1 sin )2 21

p 4 02

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Density Matrix for pure para-Density Matrix for pure para-HH22 adduct adduct

i i ii

p 1 2 3 40 0 0 0

1 sin( ) cos( )0 0

2 2 2cos( ) 1 sin( )

0 02 2 2

0 0 0 0

1

2

3

4

1

2

3

4

For ®0

(weak coupling)

0 0 0 0

1 10 0

2 21 1

0 02 2

0 0 0 0

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Adduct Density Matrix from para-H2 with mole fraction χp

10 0 0

41 sin( ) cos( )

0 04 2 2

cos( ) 1 sin( )0 0

2 4 21

0 0 04

f

f f

f f f

f

p(4 1) / 3 f 10 0 0

41

0 0 04

10 0 0

41

0 0 04

For f =0 i.e. thermalized ortho/para mixture where p = ¼ and ®0

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Pasadena correlation diagram

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Time evolution of the adduct density Matrix

d(t) H(t), (t)

dt i

†

t

t t

(t) U(t) (0)U (t)

U(t) e

(t) e (0)e

e

e e

iH

iH iH

2 2 1 1 1 1 2 2t t t t0 1 2 0(t t t ) e e (t )e e iH iH iH iH

mn

t t

t

m,n

ˆS(t) e (0)e

ˆm n n (0) m e

e eiH iH

i

Tr I

I

observed NMR signal

x y

1ˆ ˆ ˆ( )2

I I iI

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Pasadena signal from weakly coupled spin systems

y

z1 z2

I2 2

z1 z2 x1 x2 z1 x2 x1 z2

1 ˆ ˆ ˆ(0) E4

1 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ(0) E cos sin sin cos ( )4

f I I

f I I f I I f I I I I

13 3412 24 2t tt t t / TS(t, ) / 4sin cos e e e e e i ii if

Evolution under J coupling and detection:

Maximized for 45° pulse

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Obtained spectra

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Comparison to thermal signal

13 3412 24 2t tt t t / TthS (t) e e e e e

2 i ii i

0th 1z 2z

B

B1 ˆ ˆ ˆ(0) E ( ) with4 4 k T

I I

x90th 1y 2y

1 ˆ ˆ ˆ(0) E ( )4 4

I I

After 90° pulse

Evolution under J coupling and detection

13 3412 24 2t tt t t / TPasadenaS (t) sin cos e e e e e

4 i ii if

For f=1 the ratio evaluates to 2ε = 31240 !

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Altadena (just next to Pasadena)

Altadena z1 z2 z1 z2

1 1ˆ ˆ ˆ ˆ ˆE [ ( )]4 2

f I I I I

0 0 0 0

0 1 0 0

0 0 0 0

0 0 0 0

Adiabatic Longitudinal Transport After Dissociation Engenders Net Allignment

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What have we learned?

Density Matrix formalism is a very poweful tool to make accurate predictions of the NMR signals

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A step further from Hydrogenations

R1

R2para H2

R1

R2

R4

R3

R1 R3

R2 R4

+

COH2

supress relaxation !?

R1

O

R3X

R2

R1

R3

R1

R2

R2 R2

R1 R1

R1

R2

* *

etc

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Thank‘s for your attention

Thank‘s toScott Burt and Louis BouchardHattie, Pete, Ngok DoDima