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Gas-phase spin relaxation of 129Xe
Brian SaamBrian SaamDepartment of Physics
T1 = 100 hours!
Workshop on Physics & Applications of Polarized Noble GasesUniversity of Virginia, 19 May 2009
Filling the Polarization Bucket
γse
100%
PX zatio
n
PXe
Pola
ri
To maximize PX want γ >> Γ AND
Measured Γ1
0%To maximize PXe , want γse >> Γ AND <PRb> ≈ 1.
γse limited by available laser light. Measured with NMR T1
Γ =Relaxation
Goal: understand and minimize Γ.
Longitudinal Spin Relaxation in Noble Gases
1intrinsicgradientwall
1T
=Γ+Γ+Γ=Γ1
2|| BD ⊥∇=Γ
Container
K spin-rotation interaction:
B
20
gradient BD=Γ
Negligible in our experiments.1/Γwall = 0.1 – 1 h Xe
CK(R) N•K129Xe
interaction:
experiments.typically @ 30 G.
Density independent!Occurs during binary collision AND during the lifetime of a molecule.
Prior to work on dimers: Gas phase T1 typically a few tens of minutes for 129Xe; assumed dominated by wall interactions!
Early Studies of Intrinsic 129Xe Relaxation
Γ∝ [Xe]
E.R. Hunt and H.Y. Carr, Phys. Rev. 130, 2302 (1963).
Assumes binary collisions only (transient dimers).
Lowest density studied is [Xe] = 50 amagats.
Γ 0 019 h/ t (T 52 h f 1 t X )Γbulk ≈ 0.019 h/amagat (T1 ≈ 52 h for 1 atm Xe)
Transient vs. Persistent Dimers
KXeXe
ptintrinsic Γ+Γ=ΓτpCK(R) N•K XeXe
KXX
binary collisions of duration τt≈ 1 ps.
Form/break up in 3-body collisions.
L t f lif ti 1
Transient Dimers Persistent DimersXeXe
τt 1 ps.
Γt ∝ [Xe].
Γt-1 ≈ 52 h•amagat: Hunt and
Last for lifetime τp ≈ 1 ns (until next collision).
Γt is independent of [Xe](for fixed gas composition)Carr (1963); Moudrakovski, et al.
(2001).
(for fixed gas composition).
Theory of Persistent-Dimer Relaxation*
[ ]( )Xe2222
p2
22
p κ⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛
=ΓτNcK [ ]( )e
13 2p
22p κ⎟⎠
⎜⎝ Ω+⎟
⎠⎜⎝ τh
Mean-squared spin-rotation interaction energy
Chemical Equilibrium CoefficientMean-squared spin-rotation interaction energy.
Power spectrum J(ω) for field fluctuations• τp ~ 10-9 seconds for [Xe] = 1 amagat.• ω/2π = 11 8 MHz for B = 1 T
[ ][ ][ ]XeXe
Xe2≡κ
Fraction of atoms bound in molecules, assumes [Xe2] << [Xe].
• ω/2π = 11.8 MHz for B0 = 1 T.• Can often assume Ω2τp
2 << 1 (fast-fluctuation limit).
Γp is independent of [Xe]; looks like wall relaxation!⇒∝ 1τ[Xe]
Key point for SEOP regime, where Ω2τp2<< 1:
*See: B. Chann, et al., Phys. Rev. Lett. 88, 113201 (2002).
⇒τp
Low-field (2 mT) Results*
( )⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛=Γ
]Xe/[]B[111
34
]Xe[3
4
Xe2
22
p2
22
pB
KK
rkNcNc
hh
κκτ
[ ] [ ]++ BXe1 kk
XevdWΓ = pure-Xe rate Correction for 2nd gas
[ ] [ ] L++= BXe BXep
kkτ
XeBB / kkr ≡
With:
• Need constant Γwall (asymptote).
• No observed [Xe] dependence forNo observed [Xe] dependence for fixed gas composition (inset).
• ΓvdW, Γwall, rB extracted from fits.Xe
Xe
*B. Chann, et al., Phys. Rev. Lett. 88, 113201 (2002).
• ΓvdW ≈ 0.25 h-1, ten times faster than binary collisions at 1 atm!
Xe
High-field Experiments: Theory
222
⎟⎞
⎜⎛⎟
⎞⎜⎛ τNc
[ ]( )Xe213
22p
2p
2p κ⎟⎟⎠
⎞⎜⎜⎝
⎛
Ω+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=Γ
ττ
h
NcK
M ti fi ld d li tMagnetic-field decoupling term important for large Ω, small τp.
⎟⎞
⎜⎛⎟
⎞⎜⎛ 2222
22 K BNc μ Additional term due to chemical-⎟⎟⎠
⎞⎜⎜⎝
⎛Θ+⎟
⎟
⎠⎜⎜
⎝⊥22
60B
2 152
32
KK cBNc
hh
μ
Msr + Mcsa
Additional term due to chemicalshift anisotropy (CSA) interaction has dependence on .B0
2
( ) [ ]( )X2pcsasr κ⎟⎞
⎜⎛
Γτ
MM
M + M
( ) [ ]( )Xe21 2
p2
pcsasrp κ⎟
⎟⎠
⎜⎜⎝ Ω+
+=Γτ
MM
High-Field Experiment: NMR Probe & Cell
1.5 T (17.7 MHz)
Field strengths B0:( )
4.7 T (55.3 MHz)
8.0 T (94.2 MHz)
14 1 T (166 MH )
6.7 cm diam spherical “measurement” cell.
Silicone-coated.14.1 T (166 MHz)
Contains no Rb (HP gas transferred in).
Long and robust wall relaxation times.
129Xe Persistent-Dimer Relaxation: Results*
( ) [ ]( )Xe21 2
p2
pcsasrp κ⎟
⎟⎠
⎞⎜⎜⎝
⎛
Ω++=Γ
ττ
MM ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛Ω+
+=Γ 222
2csasr
p ]G[]G[2
α
ααkkMMκ
reparam.
Total gas density: ]N[]Xe[]G[ 2+=
Xe concentration (FIXED): ]G/[]Xe[≡α
Breakup coefficient: ]G[1p ατ k=−
High density: Γp independent of density.
Low density: magnetic-field T1 ≈ 5 h y gsupression of Γp.
Γp decreases for decreasing [Xe] at fixed total gas density [G].
1(wall time subtracted out).
*B.N. Berry-Pusey, et al., Phys. Rev. A 74, 063408 (2006); B.C. Anger, et al., Phys. Rev. A 78, 043406 (2008).
100-Hour Gas-Phase T1 for 129Xe
Inferred wall relaxation time:T1 (wall) = 175 h!!
Obeys the Driehuys Axiom concerning HP xenon.
Quadratic Dependence on Applied Field
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛Ω+
+=Γ 222
2csasr
p ]G[]G[2
α
ααkkMMκ
⎠⎝
Combined interaction strength of SR and CSA
Data consistent with CSA interaction strength M csa proportional to B02.
Intercept is proportional to SR interaction strength M srIntercept is proportional to SR interaction strength M .
Characteristic crossover field B0 ≈ 16 T.
So what about [Xe] = 1 amagat; B0 = 30 G?
Table II taken from: B.C. Anger, et al., Phys. Rev. A 78, 043406 (2008).
We’ve measured T1 = 5.75 h in a large 12 cm diam spherical borosilicate-glass cell (DMDCS-coated) at 30 G, 100°C. (Still limited by wall relaxation!)
Improvement to Flow-through 129Xe Polarizer*?
Long narrow cell (≈ 1 m long × 4 cm diam).g ( g )
[Xe] ≤ 1 amagat; use spectrally narrowed diode-laser array.
Counterpropagation of gas and laser light. p p g g g
Cryogenic (LN2) freeze out, separation, and storage of xenon (T1 ≈ 2.5 h @ 77 K).
*See talk B4.00002, tomorrow 10:42 am.
Goal: gas-phase storage cell (no cryogenics) with 3× storage time of frozen Xe having T1 ≈ 10 h. (Preliminary patent application filed.)
Summary
We have thoroughly (exhaustively) characterized intrinsic gas-phase T1-relaxation of 129Xe due to persistent Xe2 dimers—an important limit to production, accumulation, and storage of HP 129Xe.
Competes (and gets confused) with wall relaxation in many cases, because of
Transient-dimer contribution (binary collisions).
Persistent-dimer contribution (van der Waals molecules).
p ( g ) y ,density-independence of Γp.
Possibility of cryogen-free accumulation and storage with 2-3× longer storage times; significant improvement for state-of-the-art method in polarizing 129Xe.
Hyperpolarized Gas Research Group
FacultyBrian SaamDavid AilionGernot Laicher
Graduate StudentsBen Anger (postdoc at Leiden)Geoff Schrank (graduating Summer 2009)Geoff Schrank (graduating Summer 2009)Eric SorteZayd Ma
UndergraduatesBrittany Berry-Pusey (grad. at UCLA)Kimberly Butler (UU med. school)Laurel HalesAllison SchoeckOliver Jeong (HS student)Oliver Jeong (HS student)
Thanks to M.S. Conradi for numerous helpful discussions.
Room-Temperature Wall-Relaxation Rate vs. B0
Fast-fluctuation limitFast-fluctuation limit.
Intrinsic relaxation rate Γisubtracted out.
L t i fit i ldLorentzian fit yields correlation time for wall interaction of ≈ 4 ns.
Simple Model for Surface Relaxation of Gases
Container of 129Xe with uniformly relaxing S S ⎞⎛
V, [Xe]
uniformly relaxing stable surface
Sv
VS⎟⎠⎞
⎜⎝⎛=Γ ηwall
η
1/Γwall typically ranges from 10 to 100 min for 129Xe in carefully prepared glass vessels
η ∝ surface relaxivity
vessels.
For ballistic collisions with a uniformly relaxing surface, Γwall is independent of gas density [Xe].