Solid State NMR

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Solid State NMR

SpectroscopyPashaie.mokhtar7@gmail

.com

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

Organic complexes Inorganic complexesZeolites mesoporous solidsmicroporous solids aluminosilicates/phosphatesminerals biological moleculesGlasses cementsfood products woodceramics bonessemiconductors metals and alloysarchaelogical specimens polymersresins surfaces

Solid state NMR has been applied to

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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

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

BoSolid-state

(ordered structure)Solution-state

(random-orientation) 9

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

Shorter Spin-Spin (T2*) Relaxation

NUCLEAR MAGNETIC RESONANCE IN SOLID POLYMERS, VINCENT J. McBRIERTY, 1993.

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NMR Interactions in the Solid State

In the s

olid st

ate, a

ll of t

hese i

nterac

tions can

mak

e sec

ular

contr

ibutions. Sp

in state

energ

ies ar

e shifted re

sulting i

n direct

manife

station of t

hese i

nterac

tions in th

e NMR sp

ectra

.

1-Zeeman interaction of nuclear spins2-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

Nuclear spin interactions

The “size” of these external interactions is larger than internal

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)

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:

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

chemical shielding anisotropy gives rise to frequency shifts with the following orientation dependence:

In order to calculate powder patterns (for any anisotropicNMR interaction), one must calculate frequencies for a largenumber of orientations of the interaction tensor with respect to the magnetic field - many polar angles over a sphere: Ɵ, φ

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:

(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

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25

𝜎 ↑ ,𝐵𝑒𝑓𝑓 ↓,𝜈↓

𝜎 𝑧𝑧

𝜎 𝑥𝑥

𝜎 𝑦𝑦

𝐵 h𝑠 𝑖𝑒𝑙𝑑

𝐵𝑒𝑓𝑓 =𝐵0 −𝐵 h𝑠 𝑖𝑒𝑙𝑑

Rossum, Solid State NMR and proteins (2009)J. Duer, Solid State NMR spectroscopy (2002)

Chemical Shift Anisotropy

More shielding -> lower chemical shift

• More shielding -> lower chemical shift.

• Dependent on angular orientation

More shielded

𝜎 ↑ ,𝐵𝑒𝑓𝑓 ↓,𝜈↓

Chemical Shift Anisotropy

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Chemical Shift Anisotropy

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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

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.

Nuclear Pair Internuclear distance

Dipolar coupling

1H,1H 10 1201H,13C 1 301H,13C 2 3.8

• Dipolar coupling causes huge line broadening

J. Duer, Solid State NMR spectroscopy (2002)

Dipole-Dipole Coupling

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

B0

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

In solution, random motion averages dipolar coupling to zero

In solids, orientations are static defined by crystal lattice

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

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.

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

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 thedipolar 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!

So, for an NMR spectrum influenced only by the Zeeman and AXdipolar 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:

Presence of many dipolar interactions (e.g. between 1H’s) results in featureless spectra:

B0

rd

r

( )3 1 23

cos2

The dipolar interaction

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

in a powder, the spectra take on the famous shape known as the Pake doublet

A-A

A-Xmx= +1/2

mx= -1/2

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.

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

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).

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

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.

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:

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:

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:

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)

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

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:

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.

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

Magic Angle Spinning (MAS)

54.74o

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

Simulating the “tumbling” of molecules

http://www.rs2d.com/english/images/protasis/doty/doty.jpg

Magic Angle Spinning

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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 1cos3 2

3 rKBZ

z

y

x

1H

13C

B0

r

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.

Magic-Angle-Spinning Spectrum

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Sodium silicate glasses

BONBO

Na2Si2O5

Na2Si3O7

Na2Si4O9

600 0 -600 ppm

Static 17O NMR spectra

bridging (BO) andnon-bridging (NBO)oxygens

Structure of glasses (I)

O Si

OO

OSi O

O O

Si OO

O

Si

Si

Si

O

Si O

O

O

O

OO

OO

O

Na

Na

Na

NaSi

BO

NBO

Structure of glasses (II)

Q4

Q2

Q1Q3

O Si

HOO

OSi O

O O

Si OHHO

HO

Si

Si

Si

O

SiO

HO

HO

HO

OO

OO

O

29Si NMR spectra for sodium silicate glasses

static MASQ4

Q3 + Q2

0 -100 -200 ppm -60 -80 -100

mole %

Na2O

34

37

41

Q2

Q3

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:

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).

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

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86

87

88

89

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

90

91

Fast rotation (160 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

o7.5431cosarc

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

21cos3 2

rotor with samplein the rf coil zr

rot

θ

gradient coils forMAS PFG NMR

B0

92

Solid-state NMR spectroscopyMagic-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.

93

94

13C NMR of alanine

with1H decouplingwithout decoupling

static

spinning (5 kHz)

CH

CH3

CO2 NH3– +

CH

CH3CO2

–

* *

95

1H NMR of organic solids

Static sample

MAS

20 10 0 10proton 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

96

1H MAS NMR spectroscopy

Imidazole-MCM-41

Si

N

OH

N Si

OH

HO3S

SO3H-MCM-41

10H2O

H3O+

H2O + H+ H3O+

97

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

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

102

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 HzHartmann Hahn matching condition

DE = g h Bo / 2p

1Ha

1Hb

13Ca

13Cb

gHB1H/2p gCB1C/2p

Polarization transfer

Outline of what is happening

• Transfer of polarization from 1H to low-g nuclei

104

x

z

yx

z

yx

z

y

x

z

yx

z

yx

z

y

1H

X

(p/2)y(Spin Lock)x

(Spin Lock)x

1H

X

p/2)ySpinLock

Decouple

107

109

110

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

111

13C CP {1H} MAS NMR spectroscopy

Imidazole-MCM-41

SiHO3S

SO3H-MCM-41

NN

Si

112

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-)4Si (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.

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