1

Solids• Why spectra for solids are

broad• How to make them narrow

and informative• How to get useful info from

anisotropic interactions

Homo- and heteronuclearcouplings• Homonuclear: same kind of nuclei

• Ex. 1H-1H• Heteronuclear: different kinds of nuclei

• Ex. 1H-13C, 1H-15N

homo hetero

Abundant and dilute spins• Abundant, 1H• Isotopically dilute, 13C, 2H• Chemically dilute, 31P

DMPC, a phospholipidFig from Avanti website

homonuclearinteractions can beneglected

4

cloud of e-

chemical shielding

!

"A

=#

2$B01%&

A( )

B0

Chemical shift

ννAνBνC

Solids vs. liquids

1H shift / kHz 1H shift / ppm

cellulose + H2O surfactant in D2O

5

6

Chemical shift anisotropy (CSA)• Shift depends on relative orientation B0 -

molecular frameB0

x

y

z

δ

7

Powder patterns

δ

δ

Field from a magnetic dipole

z!

Bz"P2cos#( )r3

rθ!

P2cos"( ) =

1

23cos

2" #1( )2nd Legendre polynomial, P2

9

Dipolar coupling - anisotropic

!

"A

=#

2$B01%&

A( ) ±1

2DAXP2cos'( )

DAXP2(cosθ)

νAν

P 2(c

osθ)

B0

rθ

B0r θ

2nd Legendre polynomial, P2

Pake pattern

ν

P 2(c

osθ)

B0r θ

Δν d

/ Δν d

,max

θ / º

• One orientation: doublet• Random orientations: Pake pattern

10

90º

0º

KEMM17 VT-08, L5 11

Multiple couplings• Number of lines = 2n

• Width: “strength” of couplings

n = 1

n = 4

n = 9

12

Scalar coupling - isotropic

!

"A

=#

2$B01%&

A( ) ±1

2JAX

JAX

νAν

Origin of linewidth in solids• Anisotropic interactions

• Chemical shift anisotropy• Dipolar couplings• (Quadrupolar couplings, …)

• How to get the isotropic chemical shift?

14

Molecular motion in liquids

15

Averaging by motion

fast, isotropicreorientation

δ

• Single peak if rate of isotropicmotion >> differences in ν0

16

Rotational motion in liquids• Tumbling• Random walk on a sphere

dipole pair

P 2(c

osθ)

17

Fluctuating dipolar field, Bz

!

t "c

correlation time

P 2(c

osθ)

18

Fluctuating dipolar field, Bz

!

t "c

Average interaction = 0! (if isotropic)

P 2(c

osθ)

19

Dipolar coupling during rotation

B0

P 2(c

osθ)rotor

20

Sample spinningRotation at rate νr (~10 kHz)

B0

αR

rotor

RF coil

21

Magic angle = 54.7°

P 2(c

osθ)

Average interaction = 0 if αR = 54.7°

B0

rotor

spinningrate

θ / r

adνRt

22

Effect of spinning rate, νR

νR / DAX• Isotropic spectrum of A

if νR >> DAX, CSA• Spinning sidebands at

multiples of νR

23

Effect of spinning angle, αR

αR / °B0

αRΔν d

/ Δν d

,max

θ / º

RF decoupling• B1 field at A resonance

ν1,dec = -γB1,dec (50 kHz)• No splitting of X if ν1,A >> JAX, DAX

RF off

νXν

RF on

25

Cross-polarization (CP)• Transfer of magnetization from 1H to X

nucleus (13C, 31P, 15N, etc.)• Simultaneous B1 fields with strength ν1,H

and ν1,X at 1H and X frequencies• Resonance if ν1,H = ν1,X

Hartmann-Hahn condition

26

CP/MAS NMR• High-power 1H decoupling• Magic-angle spinning• Cross polarization

B0

54.7º

-5005010015020013C shift / ppm

DNAsugar

CTAhead

CTAtail

DNAbases

27

One strength of NMR:Switching interactions on/off• Interaction

• chemical shift• chemical shift

anisotropy• dipolar couplings

(homo, hetero)• J-couplings (homo,

hetero)• B0 inhomogeneity• …

• Tool• MAS• decoupling• spin echo• B0 strength• gradients• …

preparation evolution transfer detection

t1t2

nucleus 1

nucleus 2

Heteronuclear shift correlationHETCOR

29

Decoupling and recouplingMAS averaging would bespoiled by rotor-synchronized180° pulsesB0

rotor

Δνdip / DAX

phase / rad

νRt

Separated local field

heteronucleardipolar couplings transfer

13C isotropicshift

Separated local field161514 12 4 25 31 13N 6-11

1615

14

12

10

8

6

4

2

9

7

5

3

1

13

11

Nν 1

(1H

-13C

) / k

Hz