Solid-state NMR of spin > 1/2 - Tata Institute of ...nmr/workshops/ws_nmr_10/ssnmr_2010_files/tb... · Solid-state NMR of spin > 1/2 ... Only for spin I ≥ 1 2 H (I=1) 0 ... Multi-Quantum

TIFR/RAC, Jan. 2010 Quadrupolar Nuclei I to III

Solid-state NMR of spin > 1/2

Anisotropic Interactions

• Anisotropy of the chemical shift 1H 0 ... 40 ppm (max. 16 kHz @ 9.4 T) 13C 0 ... 250 ppm (max. 25 kHz @ 9.4 T) 19F 0 ... 300 ppm (max. 113 kHz @ 9.4 T)

• Dipolar Interaction 1H-1H, 1H-13C: typically ≤ 50 kHz

• Quadrupolar Interaction Only for spin I ≥ 1

2H (I=1) 0 ... 250 kHz

14N (I=1) 0 ... 2 MHz 23Na (I=3/2) 0 ... 10 MHz 27Al (I=5/2) 0 ... 10 MHz 35,37Cl (I=3/2) 0 ... 40 MHz

Nuclear spins with I > 1/2possess an “electricalquadrupole moment”.


Properties of Selected Quadrupolar Nuclei

Q values in millibarn


Quadrupolar Interaction for Spin-1

Energy level diagram Single crystal spectrum

Approximation:


Relative Magnitude of Quadrupolar Interaction

Different situations because of relative magnitude of quadrupolar couplingconstant Cq (or QCC, or χ) and Larmor frequency ω0:

B0 = 0: Pure quadrupolar interaction (NQR, NNuclear QQuadrupole RResonance): Transitions between the quadrupole levels

Cq « ω0: „Quadrupolar interaction of first order“(i.e., Cq of the order of tens to hundreds of kHz)

Cq ≤ ω0: „Quadrupolar interaction of 2nd (and higher) order“ (i.e., Cq of the order of MHz)

Tetrahedral and higher symmetry: eq = 0 ⇒ No quadrupolar coupling!


Quadrupolar Hamiltonian and Eigenfunctions for Spin-1

Quadrupolar Hamiltonian:

First order Hamiltonian:

Eigenvalues andEigenfunctions:

-


The Quadrupolar Splitting (I=1)

Quadrupolar CouplingConstant (QCC, Cq):

Largest component of EFG tensor:

Quadrupole moment:

!

", # Euler angles relating the PAS of the EFG to B0 (lab frame)

!

" asymmetry parameter of quadrupolar coupling tensor Q


The Quadrupolar Coupling Tensor

Keep a direct relation between doublet splitting andquadrupolar interaction by defining a quadrupolarcoupling tensor Q:

asymmetry of Q:

with:

Q in its own PAS:

with:

Obtain doublet splitting simply bythe tensor products:

b - unit vector along the magnetic field B0


From Rotation Pattern to Q-Tensor

Have z-axis of the Q-tensor PAS originally aligned alongdirection of B0, rotate step-wise around y-axis of PAS.

The tensor at 0o rotation is diagonal:


Determine Full Q-Tensor from Rotation Pattern

T. Voosegard et al.

To obtain all elements of the Q-tensor:

⇒ Need more complex transformations for general orientation of Q-tensor.

⇒ Use more than one rotation axis.

⇒ Utilize crystal symmetries to extract all information from one rotation pattern. („Single rotation method“, Tesche et al., JMR 1993)


Relation of the Q-Tensor to Molecular Structure

Haeberlen & co-workers, J. Magn. Reson., (2001), 151, 65-77. For a static (i.e. not motionallyaveraged) Q-tensor of a chemically bound deuteron, the following 3 rules can be formulated:


Dynamic Information by 2H-NMR: Relaxation Time Analysis

Reorientational correlation timesaccessible by NMR methods

T1 relaxation time curve

methyl groupdynamics

phenyl ringdynamics


The Quadrupolar Echo Sequence

Echo experiment for I=1 only!

Systematic derivation:M. H. Levitt, Spin Dynamics,2nd edition

Alternative derivation:


Solid-state 14N-NMR

S.P. Marburger, B.M. Fung, A. K. Khitrin,J. Magn. Reson. (2002) 154, 205--209

TiN(underMAS)

low symmetry:⇒ wide-line 14N-NMR spectra


14N-NMR: Overtone Spectroscopy

14N-Overtone NMR spectra of N-acetyl-D,L-valine

The frequency of a m ⇔ -m transition is unaffected by the 1st order quadrupolarsplitting. Therefore, overtone spectra of integral spin nuclei (e.g., 14N) can havemuch smaller total spectral ranges than the fundamental single-quantum spectra.


Quadrupolar Nuclei in Inorganic Materials: Mostly I > 1

Numerous materials of technologicalinterest, which are functional only in thesolid state:

• Glasses, Ceramics• Minerals, Cements• Catalysts (Zeolites)• Polymers, Biopolymers

Frequently occuringNMR-observable nuclei:

• 1H (I=1/2)• 13C (I=1/2)• 29Si (I=1/2)• 11B (I=3/2)• 17O (I=5/2)• 23Na (I=3/2)• 25Mg (I=5/2)• 27Al (I=5/2)

(2002)


Energy Levels of Spin-5/2

5(2si n22θ + si n4q)

3(si n4θ - 2si n22θ)

- 3(si n4θ - 2si n22θ)

- 5(2si n22θ + si n4θ)

2(si n4θ - 2si n22θ)

- 2(si n4θ - 2si n22θ)CT

ST

ST

ST

ST

HNMR = HZ + HQ (+ HDD + HCS) Zeeman 1st order HQ 2nd order HQ

- hν0m ( hCq/40) (3cos2θ- 1) (9hCq2/6400ν0)


Spin-5/2 Static Spectra

1st order

central transition

Spectrum with 2I components, shifted by

νm = 3Cq(3cos2θ –1)(mz –1/2 )/(4I(2I-1)), with Cq = eQVzz/h

→ quadrupolar interaction parameters can be determined from full 1st orderpattern, or from characteristic 2nd order line shape

satellite transitions

2nd order

A = (I(I +1)-3/4) νq2/ν0


Spectra of Spin-3/2 under MAS

ν r

M. E. Smith, E.R.H. van Eck, Prog. NMR Spec., 34, 159 (1999)

23Na-NMR spectra of Amelia albite (NaAlSi3O8)

2nd order line shape

2nd order quadrupolar lineshapes of the central transition

→ Extraction of quadrupolarparameters from shape ofcentral-transition line.


Signal Enhancement by Spin Population Transfer (SPT)

central transition (CT)

satellite transitions (ST)

Saturation of satellite transitions firstdemonstrated by R. V. Pound in 1950.

Experimental realisation:

• adiabatic passage (Haase et al.)

•Double Frequency Sweeps (DFS) (Kentgens et al.)

• Fast Amplitude Modulated (FAM) pulse trains (S. Vega, P. K. Madhu, A. Goldbourt; P. Grandinetti)

• hyperbolic secant pulses (HS) (Wasylishen et al.)

Signal enhancement of CT:

saturation of ST ⇒ I + 1/2

inversion of ST ⇒ 2I


Signal Enhancement using the QCPMG Sequence

87Rb (I=3/2) static


Excitation Regimes for Quadrupolar Nuclei with I > 1

Non-selective excitation:

!

"RF

>>"Q!

"Q#"

Q

(1)max( ) =

3$

2I 2I %1( )

Selective excitation:

!

"RF

<<"Q

Intermediate case:

!

"RF#"

Q


Selective Excitation of Central Transition

Pulse Nutation Response of CT:

Spin 3/2:

!

"nut

C= 2"

RF

Spin 5/2:

!

"nut

C= 3"

RF!

"nut

C= I +

1

2

#

$ %

&

' ( "RF

!

"nutC

= 2#$ nut

C % & p = 2# I +1

2

'

( )

*

+ , $RF % & p

Correct selective (“solid”) pulse:

“This effect often catches outinexperienced spectroscopists.”

(M. H. Levitt, Spin Dynamics, 2nd edition)

!

"RF

<<"Qfor


How to suppress 2nd order broadening

Simulation of 27Al-NMR MAS spectra ofthe centre band of kyanite (Al2SiO5)

B 0

M. E. Smith, E.R.H. van Eck, Prog. NMR Spec., 34, 159(1999)

field dependenceLegendre poly-nomial P4(cosq)

magi c angl e

P4(cosq)P2(cosq)

→ no angle for averaging P2and P4 simultaneously byrotating around a single axis

four sites resolved!

!"#1/ 2 , +1 / 2

(2nd order) = #Cq

2

6"0

I I +1( ) #3

4

$

% &

'

( )

* Acos4+ + Bcos

2 + + C[ ]


Averaging P4(cosθ) by Double Rotation (DOR)

“High resolution solid-state N.M.R. Averaging ofsecond-order effects by means of a double-rotor”;A. Samoson, E. Lippmaa, & A. Pines,Mol. Phys., 65, 1013 (1988)

→ mechanically demanding: limited rotation speeds, therefore limited resolution→ still impossible to extract both chemical shift and Cq from one DOR spectrum


Dynamic Angle Spinning (DAS)

B. F. Chmel ka et al ., Nature, 339, 42 (1989)

L. M. Bul l et al ., J. Am. Chem. Soc., 120, 3510 (1998)

→ less mechanically demanding than DOR→ because of long switching time (30 ms), the signal vanishes if sample has: * short T1 * strong dipolar interactions


Multi-Quantum MAS (MQMAS) Spectroscopy

MQMAS DAS

coherence order

“Isotropic Spectra of Half-Integer QuadrupoleSpins from Bidimensional MAS NMR”,L. Frydman, and J. S. Harwood,J. Am. Chem. Soc., 117, 5367 (1995)

number of citations (Jan. 2010): 731

General principle: refocus anisotropicparts of interactions, so that at kt1 anecho will form. The amplitude of thisecho evolves only under the isotropicparts of the interactions.

!"#1/ 2 ,+1 / 2

(2nd order)= !" iso

(2nd order)+ Cl

pAl $ ,%( )

l=2,4

& Pl cos'( )

k =P2cos!

1( )P2cos!

2( )=P4cos!

1( )P4cos!

2( )k =

C4

p

C4

1


Resolving Structural Sites with MQMAS

87Rb MQMAS spectra of RbNO3

D. Massiot et al., Solid State NMR, 6,73, (1996)

• anisotropic dimension F2 (2nd order quadrupolar)

• isotropic dimension F1 (chemical shift)→ different sites resolved

• obtain 2nd order line shapes for sites from 1D slices

• simulate line shapes to extract Cq values

Documents

Solid-state NMR of spin > 1/2 - Tata Institute of ...nmr/workshops/ws_nmr_10/ssnmr_2010_files/tb... · Solid-state NMR of spin > 1/2 ... Only for spin I ≥ 1 2 H (I=1) 0 ... Multi-Quantum