solids - physical chemistry · rf decoupling • b 1 field at a resonance ... switching...
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Solids• Why spectra for solids are
broad• How to make them narrow
and informative• How to get useful info from
anisotropic interactions
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Homo- and heteronuclearcouplings• Homonuclear: same kind of nuclei
• Ex. 1H-1H• Heteronuclear: different kinds of nuclei
• Ex. 1H-13C, 1H-15N
homo hetero
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Abundant and dilute spins• Abundant, 1H• Isotopically dilute, 13C, 2H• Chemically dilute, 31P
DMPC, a phospholipidFig from Avanti website
homonuclearinteractions can beneglected
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cloud of e-
chemical shielding
!
"A
=#
2$B01%&
A( )
B0
Chemical shift
ννAνBνC
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Solids vs. liquids
1H shift / kHz 1H shift / ppm
cellulose + H2O surfactant in D2O
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Chemical shift anisotropy (CSA)• Shift depends on relative orientation B0 -
molecular frameB0
x
y
z
δ
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Powder patterns
δ
δ
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Field from a magnetic dipole
z!
Bz"P2cos#( )r3
rθ!
P2cos"( ) =
1
23cos
2" #1( )2nd Legendre polynomial, P2
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Dipolar coupling - anisotropic
!
"A
=#
2$B01%&
A( ) ±1
2DAXP2cos'( )
DAXP2(cosθ)
νAν
P 2(c
osθ)
B0
rθ
B0r θ
2nd Legendre polynomial, P2
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Pake pattern
ν
P 2(c
osθ)
B0r θ
Δν d
/ Δν d
,max
θ / º
• One orientation: doublet• Random orientations: Pake pattern
10
90º
0º
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KEMM17 VT-08, L5 11
Multiple couplings• Number of lines = 2n
• Width: “strength” of couplings
n = 1
n = 4
n = 9
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Scalar coupling - isotropic
!
"A
=#
2$B01%&
A( ) ±1
2JAX
JAX
νAν
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Origin of linewidth in solids• Anisotropic interactions
• Chemical shift anisotropy• Dipolar couplings• (Quadrupolar couplings, …)
• How to get the isotropic chemical shift?
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Molecular motion in liquids
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Averaging by motion
fast, isotropicreorientation
δ
• Single peak if rate of isotropicmotion >> differences in ν0
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Rotational motion in liquids• Tumbling• Random walk on a sphere
dipole pair
P 2(c
osθ)
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Fluctuating dipolar field, Bz
!
t "c
correlation time
P 2(c
osθ)
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Fluctuating dipolar field, Bz
!
t "c
Average interaction = 0! (if isotropic)
P 2(c
osθ)
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Dipolar coupling during rotation
B0
P 2(c
osθ)rotor
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Sample spinningRotation at rate νr (~10 kHz)
B0
αR
rotor
RF coil
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Magic angle = 54.7°
P 2(c
osθ)
Average interaction = 0 if αR = 54.7°
B0
rotor
spinningrate
θ / r
adνRt
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Effect of spinning rate, νR
νR / DAX• Isotropic spectrum of A
if νR >> DAX, CSA• Spinning sidebands at
multiples of νR
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Effect of spinning angle, αR
αR / °B0
αRΔν d
/ Δν d
,max
θ / º
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RF decoupling• B1 field at A resonance
ν1,dec = -γB1,dec (50 kHz)• No splitting of X if ν1,A >> JAX, DAX
RF off
νXν
RF on
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Cross-polarization (CP)• Transfer of magnetization from 1H to X
nucleus (13C, 31P, 15N, etc.)• Simultaneous B1 fields with strength ν1,H
and ν1,X at 1H and X frequencies• Resonance if ν1,H = ν1,X
Hartmann-Hahn condition
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CP/MAS NMR• High-power 1H decoupling• Magic-angle spinning• Cross polarization
B0
54.7º
-5005010015020013C shift / ppm
DNAsugar
CTAhead
CTAtail
DNAbases
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One strength of NMR:Switching interactions on/off• Interaction
• chemical shift• chemical shift
anisotropy• dipolar couplings
(homo, hetero)• J-couplings (homo,
hetero)• B0 inhomogeneity• …
• Tool• MAS• decoupling• spin echo• B0 strength• gradients• …
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preparation evolution transfer detection
t1t2
nucleus 1
nucleus 2
Heteronuclear shift correlationHETCOR
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Decoupling and recouplingMAS averaging would bespoiled by rotor-synchronized180° pulsesB0
rotor
Δνdip / DAX
phase / rad
νRt
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Separated local field
heteronucleardipolar couplings transfer
13C isotropicshift
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Separated local field161514 12 4 25 31 13N 6-11
1615
14
12
10
8
6
4
2
9
7
5
3
1
13
11
Nν 1
(1H
-13C
) / k
Hz