Solid-state NMR Training Course

1. Solid-state NMR Training Course Introduction to the NMR of solids Paul Hodgkinson

2. CH3 CH CO2H 13 C NMR of solid alanine NMR in different phases

3. Quick NMR refresher • NMR properties of a nuclide are determined by • Spin quantum number, I • Magnetogyric ratio, g • In a magnetic field, the 2I+1 spin states are non-degenerate. Irradiation at the NMR frequency causes transitions between them: • Sensitivity is intrinsically low due to the tiny population difference between the spin states (thermal equilibrium) • Overall “receptivity” is determined by the magnitude of g and the abundance of the nuclide • “Quadrupolar” nuclei (I > ½) are more difficult to study but can be useful, especially in the solid state.

4. NMR of different nuclei v / MHz receptivity -1 7 g -1 I / 10 T s abundance 1 (at 9.4 T) (relative to H) 1 1 26. 752 H 400. 00 99. 99 % 1.00 2 1 -4 13 6. 728 1.76 ´ 10 C 100.58 1. 1 % 2 -3 14 1. 934 1.01 ´ 10 N 1 28.89 99. 6 % 1 -6 15 -2. 713 3.85 ´ 10 N 40.53 0. 37 % 2 5 -5 17 -3. 628 1.08 ´ 10 O 54.23 0. 04 % 2 1 19 25. 182 0.83 F 376.31 100 % 2 5 27 6. 976 A l 104.23 100 % 0.21 2 1 -4 29 -5. 319 3.69 ´ 10 S i 79.46 4.7 % 2 1 -2 31 10. 839 6.63 ´ 10 P 161.92 100 % 2

5. The interactions of NMR • Zeeman interaction (basic NMR phenomenon) • Shifts (interactions that change NMR frequency) • chemical shift • others (e.g. Knight shift, paramagnetic shifts) • Couplings (interactions that split NMR signals) • J coupling: often not resolved in solids • dipolar coupling: very important in solids • quadrupole coupling (VERY BIG)

6. The chemical shift

7. s B = B in d 0 æ ö s s s xx xy xz ç ÷ B s s s ind xy yy yz ç ÷ s s s è ø xz yz zz s At high field, only is significant: zz spherical angles defining anisotropy molecular orientation asymmetry isotropic shift The chemical shift (details) B 0

8. Chemical shifts in single crystals Shielding depends on molecular (i.e. crystal) orientation:

9. (Shape reflects probability of particular orientation) axial symmetry (h = 0) Powder patterns • Spectra from powdered samples are sums over individual crystallite orientations: • Well-defined powder patterns can analysed to determine chemical shift tensor components • Loss of resolution (and sensitivity) is usually unacceptable, however

10. Presence of many dipolar interactions (e.g. between 1H’s) results in featureless spectra: The dipolar interaction • Through space interaction between magnetic nuclei • Potential direct information about geometry

11. Liquids & gases: isotropic re-orientation All anisotropic terms eliminated Left with isotropic chemical shift and J Liquid crystals: anisotropic re-orientation See “residual” dipolar couplings etc. Motional averaging Rigid solids: Orientation doesn't change! See anisotropic interactions; broad lines (powder)

12. For “fast” spinning, anisotropic interactions are scaled by which is zero for b = 54.7° (magic angle) “Spinning sidebands” appear at slower speeds Magic-angle spinning • Shift anisotropy and heteronuclear dipolar interactions are easily “spun out” • Sharp centreband at isotropic shift • Sideband pattern can be analysed to quantify anisotropy • Homonuclear dipolar interactions are much harder to remove • Quadrupolar interactions are only suppressed to 1st order

13. 13C NMR • 13C is easily the most popular NMR nucleus for solids • Not affected by homonuclear or quadrupole coupling • Good chemical shift range (good for resolution) • BUT low sensitivity • Important features of 13C MAS • Magic-angle spinning removes CSA etc. • 1H decoupling to reduce broadening from dipolar coupling to 1H (requires relatively high RF powers) • Cross-polarisation from 1H greatly improves sensitivity (DCA)

14. 1 with H decoupling – CO 2 CH 3 spinning (5 kHz) CH * * 13C NMR of alanine CH 3 CH + – NH CO 3 2 without decoupling static

15. Static sample C H MAS C H 3 + N H 4 ~25 kHz MAS - 20 10 0 10 proton chemical shift (ppm) 1H NMR of organic solids 1H NMR is difficult in organic solids due to strong dipolar couplings between protons Useful resolution can be obtained, especially for H-bonded sites, with relatively fast spinning (>20 kHz) using just MAS

16. Static and dynamic “disorder” Diffraction-based methods are most suited to rigid, crystalline solids “Dynamic disorder” due to motion or “static disorder” (lack of long-range order) are not clearly distinguished Because NMR probes local environment, it is applicable to any system But “inversion” to structural information may be non-trivial Motion and disorder are readily distinguished as they have opposite effects on linewidths

17. NMR of quadrupolar nuclei

18. dipole - - + + + - interacts with interacts with electric fields field gradients The quadrupole interaction quadrupole Nuclear spins with I>1/2 have an “electric quadrupole moment”: • Size of quadrupole interaction, wQ, depends on • nucleus e.g. 2H has a relatively low quadrupole moment • symmetry of site e.g. no field gradients at cubic symmetry site • Liquids: quadrupolar nuclei relax quickly, resulting in broad lines • Solids: NMR can be complex, but may be very informative…

19. Quadrupolar nuclei: I = 1 2H NMR is often practical since the quadrupole couplings are modest The coupling shifts the energy levels resulting in a doublet for each crystallite orientation Molecular motion averages the coupling and so has a direct effect on the spectrum

20. 1st and 2nd order quadrupolar effects Quadrupole interaction (up to 10’s MHz) may not be small compared to Zeeman interaction (10’s-100’s MHz) • Central transition is unaffected to first order by quadrupole coupling • Satellite transitions often too broad to be observed

21. MAS of half-integer quadrupolar nuclei 27Al NMR of Al(NH4)(SO4)2 For modest quadrupole couplings, see intense signal from central transition + spinning sidebands from the satellite transitions

22. MAS of quadrupolar nuclei II NaCl: wQ = 0 23Na NMR of NaCl/NaNO2 mixture NaNO2: wQ = 1.09 MHz 2nd order terms degrade resolution as the quadrupolar coupling increases

23. 3 quantum transition Advanced techniques for quadrupoles I =3/2 • 1Q and 3Q transition frequencies are unaffected by 1st order quadrupole interaction • Contributions of isotropic and 2nd order components are non-zero but different • Multiple Quantum Magic-Angle Spinning (MQMAS) correlates 1Q and 3Q frequencies to separate isotropic and 2nd order effects • 2D experiment that suppresses quadrupole broadening with standard MAS hardware! +3/2 +1/2 1 quantum transition -1/2 -3/2

24. MAS MQMAS N.B. Horizontal scale varies MQMAS in action Static 23Na spectra (105.8 MHz) of sodium citrate S. C. Wimperis

25. Relaxation

26. Relaxation Spectral frequencies are not the only source of NMR information… • Spin-lattice (T1) relaxation refers to the recovery of z magnetisation to equilibrium e.g. after a pulse • T1 relaxation rates are determined by motion at the NMR frequency (i.e. 10s MHz) • T1 and other relaxation times can provide valuable information on dynamics in the solid state

27. Other relaxation times • T1 (spin-lattice relaxation in the rotating frame) • Relates to the relaxation of magnetisation held in a “spin lock” by resonant RF (cf. cross-polarisation) • Sensitive to motion on the 10s kHz scale • T2 (spin-spin relaxation) • Relaxation of transverse (xy) magnetisation • In the solution state, T2 is directly (inversely) related to linewidths • Less useful in solids as it is often impossible to distinguish linewidth due to relaxation from other effects

28. Summary • NMR of solutions is relatively straightforward • Only isotropic interactions, isotropic shift and J, are important • Chemical system is well defined (individual, equivalent molecules) • NMR of solids is rather different • More interactions are in play, especially dipolar interaction • More of the periodic table is accessible: e.g. n/2 quadrupolar nuclei • Chemical systems are often more complex • Solid-state NMR often suffers from too much information • MAS, decoupling etc. can be used to simplify spectra • Sophisticated experiments can be used to extract information of interest e.g. internuclear distances, especially in labelled samples