Nuclear Electric Quadrupolar Interactions in NMR Spectroscopy- An Introduction in NMR Spectroscopy An Introduction Hellmut Eckert I i fü Ph ik li h Ch i Institut für Physikalische Chemie WWU Münster • Electric Interactions - General • Nuclear electric quadrupole moments • Electric field gradients • The Quadrupolar Hamiltonian – NQR Spectroscopy The Quadrupolar Hamiltonian NQR Spectroscopy • Influence on the NMR Spectra – Static Solid NMR Lineshapes – MAS-NMR Spectra – Nutation Behavior – Quantification Aspects • Applications in Solid State/Materials Chemistry
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Nuclear Electric Quadrupolar Interactions in NMR Spectroscopy- An Introductionin NMR Spectroscopy An Introduction
Hellmut EckertI i fü Ph ik li h Ch iInstitut für Physikalische Chemie
WWU Münster
• Electric Interactions - General• Nuclear electric quadrupole momentsq p• Electric field gradients• The Quadrupolar Hamiltonian – NQR SpectroscopyThe Quadrupolar Hamiltonian NQR Spectroscopy• Influence on the NMR Spectra
Linewidth decreases with increasing field strengthResonance frequency increases with increasing BResonance frequency increases with increasing BoComposite shapes are field dependent
11B MAS in borate glasses
Trigonal planar D3h
Three-coord. C2v
Tetrahedral Td
23Na MQMAS @ 30kHz of crystalline Na2PO3F P t l l t d f th t f itParameters calculated from the center of gravity
Na(I): Pq = 2.3 MHziso = 2.3 ppm
ppm
-2 Na(III): Pq = 3.2 MHz 5 9
Na(II): Pq = 2.5 MHziso = 0.4 ppm
2
0
2Na(IV) IV
iso = -5.9 ppm
Na(IV): Pq = 2.7 MHziso = -4.8 ppm
2
4
6 Na(II)
Na(III)
II
III
6
8
10
Na(I)( )
I
10
12
ppm-40-30-20-100102030
14
Spectral simulation of each 23Na site resolved in the F1 dimensionin the F1 dimension
Cq = 1.98 MHziso = 3.1 ppm = 0.64
Cq = 3.0 MHziso = -6.1 ppm = 0.50Na(I) Na(III)
(ppm)-20-15-10-50510
(ppm)-55-50-45-40-35-30-25-20-15-10-5051015
Cq = 2.38 MHziso = 0.65 ppm = 0.47
Cq = 2.37 MHziso = -5.1 ppm = 0.72
Na(II)Na(IV)
( )-30-25-20-15-10-505
(ppm)-35-30-25-20-15-10-50510
(ppm) (ppm)
L. Zhang, C: Fehse, J. Vannahme, H. Eckert, to be published
Deconvolution of the MAS-NMR lineshape
Impurity NaF
(ppm)-45-40-35-30-25-20-15-10-5051015
L. Zhang, C: Fehse, J. Vannahme, H. Eckert, to be published
The intensity distribution of 1st order quadrupolar ssb-s issensitive to the EFG asymmetry parameter ( I = 7/2)
Higher Resolution in the satellite transitions
2
2 QL QS 22
L
C3 6I(I 1) 34m(m 1) 13m m g , ,128 I 2I I)
)isotropic part anisotropic part
2Q 2
QS 22 2L
C I I 1 9m m 1 33 1m 140 3I 2I 1
L I 2I 1
I = 3/2 I = 5/2 STCT CTST
2nd order effects greatly diminished for |±1/2> <-> |±3/2> coherences (I = 5/2)
A. Samoson, Chem. Phys. Lett. 119, 29 (1985)
and for |±3/2> <-> |±5/2> coherences (I = 9/2)
27Al NMR of aluminoborate glass (7.0 T)
MAS ssb
Central transition
C Jä W Müll W th C M dC. Jäger. W. Müller-Warmuth, C. Mundus, L. Van Wüllen, J. Non-cryst. Solids 149 (1992), 209
Excitation Behavior of Q-nuclei
The effective nutation frequency depends on the ratio Q/1Th t di ti t iThere are two distinct regimes:
Non selective excitation limit: << :Non-selective excitation limit: Q << 1: - Effective rf amplitude is idential to liq measured in liquids- All the Zeeman transitions are being observed.
Selective excitation limit: Q >> 1: Effective rf nutation frequency is given by (I+ ½)
g
- Effective rf nutation frequency is given by (I+ ½) liq- only the central |1/2> <-> |-1/2> coherence is detected
t1
t2 2-Dt2
detection
2-D FourierTransform
2-D Nutation NMR Spectroscopy
Kentgens et al., J. Magn. Reson. 71 (1987), 62
Spin Echo measurements of homodipole couplings between Q nucleicouplings between Q-nuclei
z y y
xx x
tD
y
x
yy dephasingyy
tD
dephasing
xx 180y (or x)
tD
refocusing
O BB O BB O BB
23Na Spin Echo Decay Spectroscopy
221(2 ) ( )IIdMI t
90° 180° t1 t1Echo
2211
0
(2 ) exp (2 )2
dMI t tI
90° 180° Echo90 180 Echot1 t1
222 cos313
90° t1 t1
Echo180°
j ij
IId r
IFM 3240
2cos31
23
4)(
Regime of validity: HQ(2) ~ HD << H1 << HQ
(1)
(selective excitation)l t t ( 100 K)low temperatures (~100 K)(no dynamic contribution)
Example of Spin Echo Curvep p
)2()2( 2 MI
2)2(
exp)0()2( 2
2dM
II
1,0
1,1
2)0(I
0 7
0,8
0,9 Rb3
ms202 for:
0,5
0,6
0,7
/I(0)
ms2,02 for:
0 2
0,3
0,4
I/
0 0 0 5 1 0 1 5 2 00,0
0,1
0,2
0,0 0,5 1,0 1,5 2,0
2 [ms]
22
23Na Spin Echo Decay: Model Compounds
18
20
22
B0=7,04T B0=9,40T
12
14
16
ad2 /s
2 ]
8
10
12
2(exp
)[106 ra
2
4
6M
2 4 6 8 10 12 14 16 18 20
2
M2(calc)[106rad2/s2]2
M = 0 9562 (µ /4)4h2r -6M2 = 0.9562 (µo/4) h rij
B.Gee, H.Eckert, Solid State Nucl. Magn. Reson. 5,113 (1995)
Spectra of spin-1/2 nuclei coupled to quadrupolar nuclei
31P MAS-NMR of (CuI) P S
quadrupolar nuclei
Cu2Cu2S3
P MAS-NMR of (CuI)3P4S4
P3
P3 P2P2P2
S1P1
S2S2P1
P2
exp fit
P1
180 160 140 120 100 80 60
[ppm]Cu1
G. Brunklaus, J. C.C. Chan, H. Eckert, S. Reiser, T. Nilges, A. Pfitzner, Phys. Chem. Chem. Phys. 5, 3678 (2003)
Practical AspectsPractical Aspects
Dipolar multiplets become asymmetric in case of strong Q-interactions
Indirect determination of CQ even if direct observationfails owing to too strong interaction
Indirect determination of CQ also possible via S{I} TRAPDOR experiments, stepping the irradiationTRAPDOR experiments, stepping the irradiationfrequency of the recouple nucleus I
S ti i 1/2 l i b d/ b blSometimes spin-1/2 nuclei are broad/unobservable, when strongly coupled with quadrupolar nuclei:certain C-N C-Cl C-Br groups in 13C CPMAScertain C-N, C-Cl, C-Br groups in C CPMAS
Further important topics• Resolution Enhancement via MQ-excitation:
A. Medek, J. S. Harwood, L. Frydman, J. Am. Chem. Soc. 1995, 117, 12779.S i l ki d CPMAS f d l l i• Spin-locking and CPMAS of quadrupolar nuclei: A. J. Vega, Solid State Nucl. Magn. Reson. 1, 16 (1992).
• Re-coupling dipolar interactions with quadrupolar nucleiT. Gullion, Chem. Phys. Lett. 1995, 246, 325. W. Strojek, M. K l i H E k t J Ph Ch B 198 7061 (2004)Kalwei, H. Eckert, J. Phys. Chem B 198, 7061 (2004)
• Signal Enhancement via Population TransferJ H M C d Ch Ph L tt 209 (1993) 287J. Haase, M. Conrady, Chem. Phys. Lett. 209 (1993), 287
• Dynamic Information via Modulation of Quadrupolar InteractionsInteractions
LiteratureLiterature• A. Abragam (1961), Principles of nuclear
magnetism, Oxford University Press.• M.H. Cohen, F. Reif, Solid State Physics 5
(1957), 321.( )• D. Freude, J. Haase, NMR-Basic Principles and
Progress 29 (1993), 3Progress 29 (1993), 3• J. Autschbach, S. Zheng, R. W. Schurko,
Concepts Magn Reson A 36 (2010) 84Concepts Magn. Reson. A 36 (2010), 84.
Signal Enhancement via Population Transfer from SatellitesTransfer from Satellites
J. Haase, M. Conrady, Chem. Phys. Lett. 209 (1993), 287
Comparison of experimental and calculated (WIEN2k) 45Sc quadrupole CQ-values in intermetallic compounds