Solid-state NMR of spin > 1/2

Transcription

1 Solid-state NMR of spin > 1/2 Nuclear spins with I > 1/2 possess an electrical quadrupole moment. Anisotropic Interactions Dipolar Interaction 1 H- 1 H, 1 H- 13 C: typically 50 khz Anisotropy of the chemical shift 1 H ppm (max T) 13 C ppm (max T) 19 F ppm (max T) Quadrupolar Interaction Only for spin I 1 2 H (I=1) khz 14 N (I=1) MHz 23 Na (I=3/2) MHz 27 Al (I=5/2) MHz 35,37 Cl (I=3/2) MHz

2 Properties of Selected Quadrupolar Nuclei Q values in millibarn

3 Quadrupolar Interaction for Spin-1 Energy level diagram Single crystal spectrum Approximation:

4 Relative Magnitude of Quadrupolar Interaction Different situations because of relative magnitude of quadrupolar coupling constant C q (or QCC, or χ) and Larmor frequency ω 0 : B 0 = 0: C q «ω 0 : C q ω 0 : Pure quadrupolar interaction (NQR, Nuclear Quadrupole Resonance): Transitions between the quadrupole levels Quadrupolar interaction of first order (i.e., Cq of the order of tens to hundreds of khz) Quadrupolar interaction of 2nd (and higher) order (i.e., Cq of the order of MHz) Tetrahedral and higher symmetry: eq = 0 No quadrupolar coupling!

5 Quadrupolar Hamiltonian and Eigenfunctions for Spin-1 Quadrupolar Hamiltonian: First order Hamiltonian: Eigenvalues and Eigenfunctions: -

6 The Quadrupolar Splitting (I=1) Quadrupolar Coupling Constant (QCC, C q ): Largest component of EFG tensor: Quadrupole moment: ", # Euler angles relating the PAS of the EFG to B 0 (lab frame) " asymmetry parameter of quadrupolar coupling tensor Q

7 The Quadrupolar Coupling Tensor Keep a direct relation between doublet splitting and quadrupolar interaction by defining a quadrupolar coupling tensor Q: asymmetry of Q: with: Q in its own PAS: Obtain doublet splitting simply by the tensor products: b - unit vector along the magnetic field B 0 with:

8 From Rotation Pattern to Q-Tensor Have z-axis of the Q-tensor PAS originally aligned along direction of B 0, rotate step-wise around y-axis of PAS. The tensor at 0 o rotation is diagonal:

9 Determine Full Q-Tensor from Rotation Pattern To obtain all elements of the Q-tensor: Need more complex transformations for general orientation of Q-tensor. Use more than one rotation axis. T. Voosegard et al. Utilize crystal symmetries to extract all information from one rotation pattern. ( Single rotation method, Tesche et al., JMR 1993)

10 Relation of the Q-Tensor to Molecular Structure Haeberlen & co-workers, J. Magn. Reson., (2001), 151, For a static (i.e. not motionally averaged) Q-tensor of a chemically bound deuteron, the following 3 rules can be formulated:

11 Dynamic Information by 2 H-NMR: Relaxation Time Analysis Reorientational correlation times accessible by NMR methods phenyl ring dynamics methyl group dynamics T 1 relaxation time curve

12 The Quadrupolar Echo Sequence Echo experiment for I=1 only! Systematic derivation: M. H. Levitt, Spin Dynamics, 2 nd edition Alternative derivation:

13 Solid-state 14 N-NMR TiN (under MAS) low symmetry: wide-line 14 N-NMR spectra S.P. Marburger, B.M. Fung, A. K. Khitrin, J. Magn. Reson. (2002) 154,

14 14 N-NMR: Overtone Spectroscopy 14 N-Overtone NMR spectra of N-acetyl-D,L-valine The frequency of a m -m transition is unaffected by the 1 st order quadrupolar splitting. Therefore, overtone spectra of integral spin nuclei (e.g., 14 N) can have much smaller total spectral ranges than the fundamental single-quantum spectra.

15 Quadrupolar Nuclei in Inorganic Materials: Mostly I > 1 Numerous materials of technological interest, which are functional only in the solid state: Glasses, Ceramics Minerals, Cements Catalysts (Zeolites) Polymers, Biopolymers Frequently occuring NMR-observable nuclei: (2002) 1 H (I=1/2) 13 C (I=1/2) 29 Si (I=1/2) 11 B (I=3/2) 17 O (I=5/2) 23 Na (I=3/2) 25 Mg (I=5/2) 27 Al (I=5/2)

16 Energy Levels of Spin-5/2 H NMR = H Z + H Q (+ H DD + H CS ) Zeeman 1 st order H Q 2 nd order H Q - hν 0 m ( hc q /40) ( 3cos 2 θ- 1) ( 9hC q2 /6400ν 0 ) 5( 2si n 2 2θ + si n 4 q) ST ST CT ST ST 3( si n 4 θ - 2si n 2 2θ) 2( si n 4 θ - 2si n 2 2θ) - 2( si n 4 θ - 2si n 2 2θ) - 3( si n 4 θ - 2si n 2 2θ) - 5( 2si n 2 2θ + si n 4 θ)

17 Spin-5/2 Static Spectra 1 st order 2 nd order central transition satellite transitions Spectrum with 2I components, shifted by A = (I(I +1)-3/4) ν q 2 /ν 0 ν m = 3C q (3cos 2 θ 1)(m z 1/2 )/(4I(2I-1)), with C q = eqv zz /h quadrupolar interaction parameters can be determined from full 1 st order pattern, or from characteristic 2 nd order line shape

18 Spectra of Spin-3/2 under MAS 23 Na-NMR spectra of Amelia albite (NaAlSi 3 O 8 ) 2 nd order quadrupolar line shapes of the central transition 2 nd order line shape ν r M. E. Smith, E.R.H. van Eck, Pr og. NMR Spec., 34, 159 (1999) Extraction of quadrupolar parameters from shape of central-transition line.

19 Signal Enhancement by Spin Population Transfer (SPT) central transition (CT) Saturation of satellite transitions first demonstrated by R. V. Pound in Experimental realisation: adiabatic passage (Haase et al.) Double Frequency Sweeps (DFS) (Kentgens et al.) satellite transitions (ST) Signal enhancement of CT: saturation of ST I + 1/2 inversion of ST 2I Fast Amplitude Modulated (FAM) pulse trains (S. Vega, P. K. Madhu, A. Goldbourt; P. Grandinetti) hyperbolic secant pulses (HS) (Wasylishen et al.)

20 Signal Enhancement using the QCPMG Sequence 87 Rb (I=3/2) static

21 Excitation Regimes for Quadrupolar Nuclei with I > 1 " Q # " (1) Q ( max) = Non-selective excitation: " RF >> " Q 3$ 2I 2I %1 ( ) Selective excitation: " RF << " Q Intermediate case: " RF # " Q

22 Selective Excitation of Central Transition Pulse Nutation Response of CT: # C = I + 1 & % (" $ 2' RF " nut for " RF << " Q Spin 3/2: Spin 5/2: " C nut " C nut = 2" RF = 3" RF This effect often catches out inexperienced spectroscopists. (M. H. Levitt, Spin Dynamics, 2 nd edition) Correct selective ( solid ) pulse: ' " C nut = 2#$ C nut % & p = 2# ) I + 1 *, $ ( 2+ RF % & p

23 How to suppress 2 nd order broadening Simulation of 27 Al-NMR MAS spectra of the centre band of kyanite (Al 2 SiO 5 ) four sites resolved! (2nd!" order) #1/ 2, +1 / 2 = # C 2 q $ & I I +1 6" 0 % ( ) # 3 4 ' ) ( [ ] * Acos Bcos C field dependence Legendr e polynomial P 4 (cosq) B 0 P 2 (cosq) P 4 (cosq) magi c angl e M. E. Smith, E.R.H. van Eck, Pr og. NMR Spec., 34, 159 (1999) no angle for averaging P 2 and P 4 simultaneously by rotating around a single axis

24 Averaging P 4 (cosθ) by Double Rotation (DOR) High resolution solid-state N.M.R. Averaging of second-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 C q from one DOR spectrum

25 Dynamic Angle Spinning (DAS) B. F. Chmel ka et al., Nature, 339, 42 ( 1989) less mechanically demanding than DOR because of long switching time (30 ms), the signal vanishes if sample has: * short T 1 * strong dipolar interactions L. M. Bul l et al., J. Am. Chem. Soc., 120, 3510 ( 1998)

26 Multi-Quantum MAS (MQMAS) Spectroscopy (2nd!" order) (2nd #1/ 2, +1 / 2 =!" order) iso + & C p l A l ( $,% ) P l cos' l =2,4 ( ) MQMAS k = C 4 p C 4 1 coherence order DAS ( ) ( ) = P cos! 4 ( 1) ( ) k = P cos! 2 1 P 2 cos! 2 P 4 cos! 2 Isotropic Spectra of Half-Integer Quadrupole Spins 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 anisotropic parts of interactions, so that at kt 1 an echo will form. The amplitude of this echo evolves only under the isotropic parts of the interactions.

27 Resolving Structural Sites with MQMAS 87 Rb MQMAS spectra of RbNO 3 D. Massiot et al., Solid State NMR, 6, 73, (1996) anisotropic dimension F2 (2 nd order quadrupolar) isotropic dimension F1 (chemical shift) different sites resolved obtain 2 nd order line shapes for sites from 1D slices simulate line shapes to extract C q values