solid state nmr spectroscopy

2. ‫ز‬‫و‬‫ر‬‫و‬‫شب‬ ‫و‬‫آمد‬ ‫و‬‫فت‬‫ر‬ ‫و‬‫مین‬‫ز‬ ‫و‬‫آسمانها‬‫آفرینش‬ ‫در‬ ‫همانا‬‫عقل‬‫صاحبان‬ ‫ای‬‫ر‬‫ب‬‫است‬ ‫هایی‬ ‫نشانه‬.
(‫ان‬‫ر‬‫عم‬ ‫آل‬ ‫سوره‬:190)

3. Solid State NMR
Spectroscopy
Pashaie.mokhtar7@gmail.com

4. Solid State NMR Applications
 The very powerful technique for amorphous solids, powder crystalline samples.
 Determination of local molecular environments.
 measurement of internuclear distances (dipolar recoupling)
 Structure
 Chirality
 Enzyme mechanisms
 Polymorphism

5. Organic complexes Inorganic complexes
Zeolites mesoporous solids
microporous solids aluminosilicates/phosphates
minerals biological molecules
Glasses cements
food products wood
ceramics bones
semiconductors metals and alloys
archaelogical specimens polymers
resins surfaces
Solid state NMR has been applied to

6. 6
13C NMR of glycine
Adapted from M. Edén, Concepts in Magnetic Resonance 18A, 24.
D. Lide, G. W. A. Milne, Handbook of Data on Organic Compounds:
Compounds 10001-15600 Cha-Hex. (CRC Press, 1994).
Solid Liquid
Powder Spectra

9. Solid and Liquid
• Factors that average to zero in solution due to random motion are now factors in
solid state NMR
• T1 is long  lack of motion and modulation of dipole-dipole interaction
• T2 is short  mutual spin flips occurring between pairs of spins
 Each nucleus produces a rotating magnetic field as it precesses in the applied
magnetic field
 Each spin has a static field component that influences Larmor frequency of
neighbors
- Range of frequencies that add to line-width
Chemical shift anisotropy
- Chemical shift varies with orientation relative to B0
Bo
Solid-state
(ordered structure)
Solution-state
(random-orientation) 9

10. Line-shape Broadening Factors for Solid Samples
 Direct Dipolar Coupling
◦ Between at least two nuclear magnetic moments
◦ Heteronuclear and Homonuclear
 Chemical Shift Anisotropy
◦ Orientation dependence of molecule relative to Bo
 Shorter Spin-Spin (T2*) Relaxation
◦ Larger linewidths at half-height
 Quadrupolar Interaction for Spin > ½
◦ Between nuclear charge distribution and electric field gradient in the solid
 Magnetic Susceptibility
◦ Differences of Ho (mag. flux) at solid / liquid interface

11. Shorter Spin-Spin (T2*) Relaxation
NUCLEAR MAGNETIC RESONANCE IN SOLID POLYMERS, VINCENT J. McBRIERTY, 1993.

12. NMR Interactions in the Solid State
12
1-Zeeman interaction of nuclear spins
2-Direct dipolar spin interaction
3-Indirect spin-spin coupling (J-
coupling), nuclear-electron spin coupling
(paramagnetic),
coupling of nuclear spins with molecular
electric field gradients (quadrupolar
interaction).
4-Direct spin-lattice interactions
3,5-Indirect spin-lattice interaction via
electrons
3,6-Chemical shielding and polarization of
nuclear spins by electrons
4,7-Coupling of nuclear spins to sound fields

14. Nuclear spin interactions
The “size” of these external interactions is larger than internal

15. All NMR interactions are anisotropic - their three dimensional nature can be described
by second-rank Cartesian tensors, which are 3 × 3 matrices.
The NMR interaction tensor describes the orientation of an NMR interaction with
respect to the cartesian axis system of the molecule.
These tensors can be diagonalized to yield tensors that have three principal
components which describe the interaction in its own principal axis system (PAS)

17. Zeeman interaction
 It can be described with a Hamiltonian
• or in ternsor form
 In the magnetic field the two spin states
have different energies
 It is far the strongest interaction and all
other types of interaction can be
considered as corrections
 Order of the magnitude:

19. Chemical shielding is an anisotropic interaction characterized by a shielding tensor σ,
which can also be diagonalized to yield a tensor with three principal components.
Isotropic Chemical shielding

21. chemical shielding anisotropy gives rise to frequency shifts with the
following orientation dependence:
In order to calculate powder
patterns (for any anisotropic
NMR interaction), one must
calculate frequencies for a large
number of orientations of the
interaction tensor with respect
to the magnetic field - many
polar angles over a sphere: Ɵ, φ

22. Chemical shifts in single crystals
Shielding depends on molecular (i.e. crystal) orientation:
s
q
23

23. Powder patterns
• Spectra from powdered samples are sums over individual crystallite
orientations:
(Shape reflects probability of
particular orientation)
axial symmetry (h = 0)
 Well-defined powder patterns can analysed to determine chemical
shift tensor components
 Loss of resolution (and sensitivity) is usually unacceptable
24

24. 25

25. 𝜎 ↑, 𝐵 𝑒𝑓𝑓 ↓, 𝜈 ↓
𝜎𝑧𝑧
𝜎 𝑥𝑥
𝜎 𝑦𝑦
𝐵𝑠ℎ𝑖𝑒𝑙𝑑
𝐵𝑒𝑓𝑓 = 𝐵0 − 𝐵𝑠ℎ𝑖𝑒𝑙𝑑
Rossum, Solid State NMR and proteins (2009)
J. Duer, Solid State NMR spectroscopy (2002)
Chemical Shift Anisotropy
More shielding -> lower chemical shift

26. • More shielding -> lower
chemical shift.
• Dependent on angular orientation
More shielded
𝜎 ↑, 𝐵 𝑒𝑓𝑓 ↓, 𝜈 ↓
Chemical Shift Anisotropy

27. 28
Chemical Shift Anisotropy

28. Powder Pattern
 Chemical shift is dependent on orientation of nuclei in the solid
- Distribution of chemical shifts
- Averaged to zero for isotropic tumbling
- Leads to extensive line-width broadening in solid-state NMR
Progress in Nuclear Magnetic Resonance Spectroscopy 6 46 (2005) 1–21
29

31. Why is the chemical shift orientation dependent?
Molecules have definite 3D shapes, and certain electronic circulations (which induced the
local magnetic fields) are preferred over others. Molecular orbitals and crystallographic
symmetry dictate the orientation and magnitude of chemical shielding tensors.

34. Nuclear Pair Internuclear
distance [Å]
Dipolar
coupling [𝒌𝑯𝒛]
1H,1H 10 120
1H,13C 1 30
1H,13C 2 3.8
• Dipolar coupling causes huge line broadening
J. Duer, Solid State NMR spectroscopy (2002)
Dipole-Dipole Coupling

35. When two spins (nuclei I and S) are close (≤10 Å) in a magnetic field ...
◦ One spin affects local magnetic field at another spin
◦ Changes frequency of paired nuclei
◦ Interaction depends on I-S distance and angle between I-S and Bo
z
y
x
1H
13C
qB0
r
 The degree by which spin I affects the magnetic field at spin S is determined by the
dipolar coupling constant (d):
  zzIS SIdH 1cos3 2
 q
In solution, random motion averages dipolar coupling to zero
In solids, orientations are static  defined by crystal lattice

36. Direct dipole coupling
 Useful for molecule structure
studies and provides a good
way to estimate distances
between nuclei and hence the
geometrical form of the
molecule

37. The dipolar interaction results from interaction of one nuclear spin with a magnetic
field generated by another nuclear spin, and vice versa. This is a direct through
space interaction.

38. Dipolar hamiltonian can be expanded into the dipolar alphabet, which has both spin operators
and spatially dependent terms. Only term A makes a secular contribution for heteronuclear
spin pairs, and A and B (flip flop) both make contributions for homonuclear spin pairs:
HDD=A+B+C+D+E+F

39. In a solid-state powder sample
every magnetic spin is coupled to every other magnetic spin; dipolar couplings serve to
severely broaden NMR spectra.
In solution
molecules reorient quickly; nuclear spins feel a time average of the spatial part of the
dipolar interaction +3cos2 2-1, over all orientations 2,N.
The dipolar interaction tensor is symmetric and traceless, meaning that the interaction
is symmetric between the two nuclei, and there is no isotropic dipolar coupling:
For a heteronuclear spin pair in the solid state, the (3cosƟ2 - 1) term is not averaged
by random isotropic tumbling: the spatial term will have an effect on the spectrum!

40. So, for an NMR spectrum influenced only by the Zeeman and AX
dipolar interaction, the frequencies for A can be calculated as:
For a homonuclear spin pair, the flip flop term (B) is also important:
So the frequencies of the transitions can be calculated as:

41. Presence of many dipolar
interactions (e.g. between 1H’s)
results in featureless spectra:
B0
q r
d
r
µ
-( )3 1 2
3
cos2
q
The dipolar interaction

42. In a single crystal with one orientation of dipolar vectors, a single set of
peaks would be observed

43. in a powder, the spectra take on the famous shape known as the Pake doublet
A-A
A-X
mx= +1/2
mx= -1/2

44. The Pake doublet was first observed in the 1H NMR spectrum of solid CaSO4.H2O. The Pake
doublet is composed of two subspectra resulting from the α and β spin states of the coupled
nucleus.

49. J-coupling
 Nuclear spins are coupled with the help of the molecular electrons
 It is exclusively intramolecular
 The mechanism responsible for the multiplet structure It can be
viewed only in solution-state NMR spectra where the spectral lines
are narrow enough to observe the interaction

52. Notably, NMR of half-integer quadrupolar nuclei has become quite commonplace, and
allowed investigation of a broad array of materials. The only integer quadrupolar nuclei
investigated regularly are 2H (very common) and 14 N (less common).

53. Electric Quadrupole Coupling
 Nucleus with the electric quadrupole moment interacts strongly with the
electric field gradients generated by surrounding electron clouds
 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…
Quadrupole interaction is totaly averaged in liquids, but in solids is the strongest
after Zeeman
 In solids we often need to take into account second order contributions

54. an asymmetric distribution of nucleons giving rise to a non-spherical
positive electric charge distribution
The asymmetric charge distribution in the nucleus is described by the nuclear electric
quadrupole moment, eQ, which is measured in barn (which is ca. 10-28 m2 ). eQ is an
instrinsic property of the nucleus, and is the same regardless of the environment.

55. Quadrupolar nuclei interact with electric field gradients (EFGs) in the molecule: EFGs are
spatial changes in electric field in the molecule. Like the dipolar interaction, the quadrupolar
interaction is a ground state interaction, but is dependent upon the distribution of electric
point charges in the molecule and resulting EFGs.
The EFGs at the quadrupolar nucleus can be described by a symmetric traceless
tensor, which can also be diagonalized:

56. The magnitude of the quadrupolar interaction is given by the nuclear quadrupole coupling
constant:
For a quadrupolar nucleus in the centre of a spherically symmetric molecule, the EFGs cancel
one another resulting in very small EFGs at the quadrupolar nucleus. As the spherical
symmetry breaks down, the EFGs at the quadrupolar nucleus grow in magnitude:

57. The quadrupolar interaction, unlike all of the other anisotropic NMR interactions,
can be written as a sum of first and second order interactions:
Below, the effects of the first- and second-order interactions on the energy levels of a
spin -5/2 nucleus are shown:

58. The first order interaction is proportional to CQ, and the second-order interaction
is proportional to CQ
2/ν0, and is much smaller.
Notice that the first-order interaction does not affect the central transition.
The first-order quadrupolar interaction is described by the hamiltonian
(where Ɵ and φ are polar angles)

59. Perturbation theory can be used to calculate the second-order shifts in energy levels
(note that this decreases at higher fields)

60. only the first-order quadrupolar
interaction is visible, with a sharp
central transition, and various
satellite transitions that have
shapes resembling axial CSA
patterns.
Static spectra of quadrupolar nuclei are shown below for the case of spin 5/2:

61. the value of CQ is much larger. The satellite
transitions broaden and disappear and
only the central transition spectrum is left
(which is unaffected by first-order
interactions). It still has a strange shape
due to the orientation dependence of the
second- order quadrupolar frequency.

62. A number of methods have been developed and considered in order to minimize large
anisotropic NMR interactions between nuclei and increase S/N in rare spin (e.g., 13 C, 15 N)
NMR spectra
High-Resolution Solid-State NMR
Magic-angle spinning
Cross Polarization

63. Magic Angle Spinning (MAS)
54.74o

64. Notice that the dipolar and chemical shielding interactions both
contain 3cos2 Ɵ - 1 terms.
In solution, rapid isotropic tumbling averages this spatial
component to zero.
Magic-angle spinning introduces artificial motion by placing the
axis of the sample rotor at the magic angle (54.74) with respect to
B0 - the term 3cos2 Ɵ - 1 = 0 when θ = 54.74.
The rate of MAS must be greater than or equal to the magnitude of
the anisotropic interaction to average it to zero.
Magic-angle spinning

66. Simulating the “tumbling” of molecules
http://www.rs2d.com/english/images/protasis/doty/doty.jpg
Magic Angle Spinning

67. Magic Angle Spinning (MAS)
• Zero z component (Bz) if the angle (q) relative to B0 is 54.7356°
• All dipolar interactions disappear at this angle
 All chemical shift anisotropy disappear at this angle
 Quadrupole broadening is also reduced
 Simulate a uniform distribution of magnetic moments in a powder by
spinning the sample very fast at 54.44o
Bz = 0
68
 1cos3 2
3
 q

r
K
BZ
z
y
x
1H
13C
qB0
r

68. Samples are finely powdered and packed tightly into rotors, which are then spun at rates
from 1 to 35 kHz, depending on the rotor size and type of experiment being conducted.
If the sample is spun at a rate less than the magnitude of the anisotropic interaction, a
manifold of spinning sidebands becomes visible, which are separated by the rate of
spinning (in Hz).
Here is an example of MAS applied in a 31 P CPMAS NMR experiment: The span of this
spectrum is S . 500 ppm, corresponding to a breadth of about 40000 Hz (31 P at 4.7
T). The isotropic centreband can be identified since it remains in the same position at
different spinning rates.

71. Magic-Angle-Spinning Spectrum

72. 73

73. Sodium silicate glasses
BO
NBO
Na2Si2O5
Na2Si3O7
Na2Si4O9
600 0 -600 ppm
Static 17O NMR spectra
bridging (BO) and
non-bridging (NBO)
oxygens

74. Structure of glasses (I)
O
Si
O
O
O
Si
O
O O
Si
OO
O
Si
Si
Si
O
Si O
O
O
O
O
O
O
O
O
Na
Na
Na
Na
Si
BO
NBO

75. Structure of glasses (II)
Q4
Q2
Q1Q3
O
Si
HO
O
O
Si
O
O O
Si
OHHO
HO
Si
Si
Si
O
Si
O
HO
HO
HO
O
O
O
O
O

76. 29Si NMR spectra for sodium silicate glasses
static MAS
Q4
Q3 + Q2
0 -100 -200 ppm -60 -80 -100
mole %
Na2O
34
37
41
Q2
Q3

77. Unlike first-order interactions, the second-order term is not averaged to zero by
MAS. The second-order quadrupolar frequency can be expressed in terms of
zeroth-, second- and fourth-order Legendre polynomials:

78. So the second-order quadrupolar interaction cannot be completely averaged unless the rotor
is spun about two axes simultaneously at β = 30.55° and 70.12°.
There are experiments called DOR(double rotation - actual special probe that does this)
and DAS (dynamic angle spinning - another special probe).

83. Decoupling
static
static with low
power decoupling
static with high
power decoupling
decoupling + MAS
solution-state
spectrum
• In the mechanism of decoupling a
strong rf field is applied so that
magnetic moments are flipped
randomely back and forth to narrow
the anisotropic broadeneng of the
resonance lines
84

84. 85

85. 86

86. 87

87. 88

88. Magic Angle Spinning (MAS)
• Spin Samples at 54.44o to reduce line-width
 Spinning speed must be greater than static line-width to be studied
(powder pattern width)
- Normal speed limit is 35 kHz
Sample holder rotor
Sample holder at MAS MAS probe
rotor at MAS
89

89. 90

90. Fast rotation (160 kHz) of the sample about an
axis oriented at 54.7° (magic-angle) with respect
to the static magnetic field removes all
broadening effects with an angular dependency
of
o
7.54
3
1
cosarc q
That means
chemical shift anisotropy,
dipolar interactions,
first-order quadrupole interactions, and
inhomogeneities of the magnetic
susceptibility.
It results an enhancement in spectral
resolution by line narrowing also for soft
matter studies.
High-resolution solid-state MAS NMR
2
1cos3 2
q
rotor with sample
in the rf coil zr
rot
θ
gradient coils for
MAS PFG NMR
B0
91

91. Solid-state NMR spectroscopy
Magic-angle spinning NMR spectroscopy on 1H, 13C, and 29Si nuclei in the functionalized
mesoporous proton conducting materials was performed in
the fields of 9.4 and 17.6 Tesla mainly at room temperature.
92

92. 93

93. 13C NMR of alanine
with 1
H decouplingwithout decoupling
static
spinning (5 kHz)
CH
CH3
CO2 NH3
– +
CH
CH3
CO2
–
* *
94

94. 1H NMR of organic solids
Static sample
MAS
20 10 0 10
proton chemical shift (ppm)
~25 kHz MAS
NH4
CH CH3+
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
95

95. 1H MAS NMR spectroscopy
Imidazole-MCM-41
Si
N
O
H
N Si
O
H
HO3S
SO3H-MCM-41
 10
H2O
H3O+
H2O + H+  H3O+
96

96. MAS reduces linewidth
from 5000 Hz to 200 Hz
High power decoupling
reduces linewidth from
5000 Hz to 450 Hz
MAS & high power decoupling
reduces linewidth from 5000
Hz to 2 Hz
Similar to liquid state sample
Spin ½ Nuclei with Low Magnetogyric ratios (13C, 15N, 29Si, 31P, 113Cd)
• Combine MAS with high power 1H decoupling
 High power is required because of very large 1H line-widths
- Low sensitivity of nuclei requires long acquisition times
97

97. Cross polarization is one of the most important techniques in solid state NMR. In
this technique, polarization from abundant spins such as 1H or 19F is transferred
to dilute spins such as 13C or15N. The overall effect is to enhance S/N:
1. Cross polarization enhances signal from dilute spins potentially by a factor of γI/γS
where I is the abundant spin and S is the dilute spin.
2. Since abundant spins are strongly dipolar coupled, they are therefore subject to large
fluctuating magnetic fields resulting from motion. This induces rapid spin-lattice relaxation
at the abundant nuclei.
Polarization is transferred during the spin locking period, (the contact time) and a П/2
pulse is only made on protons:
the proton and carbon magnetization precess in the rotating frame at the same rate,
allowing for transfer of the abundant spin polarization to carbon
Cross Polarization

98. Cross-polarization combined with MAS (CP-MAS)
• Exchange polarization from 1H to 13C
2 ms 50 ms
• 1H 90o pulse generates xy magnetization (B1H)
• Spin-lock pulse keeps magnetization in xy plane
precessing at:
gHB1H/2p Hz
• 13C pulse generates xy magnetization that precesses
at:
gCB1C/2p Hz
• Polarization transfer occurs if:
gHB1H/2p Hz = gCB1C/2p Hz
Hartmann Hahn matching condition
DE = g h Bo / 2p
1Ha
1Hb
13Ca
13Cb
gHB1H/2p gCB1C/2p
Polarization transfer
102

100. Outline of what is happening
• Transfer of polarization from 1H to low-g nuclei
104
x
z
y
x
z
y
x
z
y
x
z
y
x
z
y
x
z
y
1H
X
(p/2)y
(Spin Lock)x
(Spin Lock)x
1H
X
p/2)y
Spin
Lock
Decouple

103. 107

104. 109

105. Cross-polarization combined with MAS (CP-MAS)
• Example of CP-MAS 13C spectrum
 Cross-polarization increases the 13C population difference by the factor gH/gC
 Increases signal sensitivity
110

106. 111

107. 13C CP {1H} MAS NMR spectroscopy
Imidazole-MCM-41
SiHO3S
SO3H-MCM-41
N
N
Si
112

108. 29Si CP {1H} MAS NMR spectroscopy
Imidazole-MCM-41
29Si CP {1H} MAS NMR
29Si MAS NMR (one-pulse)
Si (OSi-)3 (OH)1
Si (OSi-)4
Si (OSi-)2 (OH)2
-CH2Si (OSi-)2 (OH)1
-CH2Si (OSi-)3
100%5% 5%
relative concentration
29Si MAS NMR Bloch decay spectra yield
quantitative information
about linking of functional groups.
113