Solid-state NMR Training Course

1
Solid-state NMR Training Course
Introduction to the NMR of solids
Paul Hodgkinson
2
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 2I1 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 gt ½) are more difficult
  to study but can be useful, especially in the
  solid state.

4
NMR of different nuclei
v
/ MHz
receptivity
7
-1
g
-1
/ 10
T
s
I
abundance
1
(at 9.4 T)
(relative to
H)
1
1
26.
752
H
400.
00
1.00
99.
99
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
0.21
100
2
1
-4
29
-5.
319
3.69

10
S
i
79.46
4.7
2
1
31
-2
10.
839
6.63

10
P
100
161.92
2
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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)

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The chemical shift
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The chemical shift (details)
B
0
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Chemical shifts in single crystals

• Shielding depends on molecular (i.e. crystal)
  orientation

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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

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The dipolar interaction

• Through space interaction between magnetic
  nuclei
• Potential direct information about geometry

11
Motional averaging
Rigid solids Orientation doesn't change!
See anisotropic interactions broad lines (powder)
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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

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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
13C NMR of alanine
CH
3
CH


NH
CO
2
3
without decoupling
static
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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
(gt20 kHz) using just MAS
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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
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NMR of quadrupolar nuclei
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The quadrupole interaction
quadrupole

• Nuclear spins with Igt1/2 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

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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
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1st and 2nd order quadrupolar effects
Quadrupole interaction (up to 10s MHz) may not
be small compared to Zeeman interaction
(10s-100s MHz)

• Central transition is unaffected to first order
  by quadrupole coupling
• Satellite transitions often too broad to be
  observed

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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
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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
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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
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MQMAS in action
Static
23Na spectra (105.8 MHz) of sodium citrate S. C.
Wimperis
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Relaxation
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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

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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

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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