11-1

Nuclear Magnetic Resonance• Absorption of electromagnetic radiation from 4 MHz to 900 MHz• Nuclear process

Radiation absorbed by nuclei• Sample must be placed in strong magnetic field• Used for determining structure• Two types of NMR

Continuous wave Pulsed wave

Most spectrometers are pulsed wave (FT)

Theory Environmental effects on spectra Spectrometers Applications

11-2

Theory• Quantum description

Spin Nuclei with spin have angular momentum (p)

p is integral or half integral multiple of h/2 For a given p, maximum spin values is I

* Spin quantum number Nuclei has 2I+1 states

* m=I, I-1, ….., -I States energies differ in magnetic field

• For proton p=1/2 m= ½, -1/2

11-3

Energy levels

• Magnetic moment becomes orientated in two directions

½ is lower E, -1/2 is higher + or - B

hE

4

00 2

hEfromB

11-4

Distribution

• What is distribution between states Based on Boltzmann’s equation

• For proton in 4.69 T field at 20 °C

)2

exp(2/1

2/1

kT

hB

N

N

999967.0)293*2338.12

69.4*3463.6*868.2exp(

2/1

2/1

E

Ee

N

N

000033.12/1

2/1 N

N

11-5

Nuclei properties

isotope spin I natural abundance [%]

gyromagnetic ratio, (gamma) [107*rad/(T*s)]

relative sensitivity

absolute sensitivity

1H 1/2 99.98 26.7519 1.00 1.00

2H 1 0.016 4.1066 9.65 · 10-6 1.45 · 10-6

12C 0 98.9 -- -- --

13C 1/2 1.108 6.7283 1.59 · 10-2 1.76 · 10-4

14N 1 99.63 1.9338 1.01 · 10-3 1.01 · 10-3

15N 1/2 0.37 -2.712 1.04 · 10-3 3.85 · 10-6

16O 0 98.9 -- -- --

17O 5/2 0.037 -3.6279 2.91 · 10-2 1.08 · 10-5

31P 1/2 100 10.841 6.63 · 10-2 6.63 · 10-2

11-6

Theory

• Magnetic moment related to magnetogyric ratio () p

11-7

Procession in a magnetic field

• Angular velocity (radians/s)

• Larmor frequency

2

B

11-8

Relaxation Process

• Non-radiative relaxation processes (thermodynamics!). If the relaxation rate is fast, then saturation is

reduced If the relaxation rate is too fast, line-broadening in

the resultant NMR spectrum is observed

• Two major relaxation processes; Spin - lattice (longitudinal) relaxation

T1 relaxation time

Spin - spin (transverse) relaxation

11-9

Spin Lattice Relaxation

• Nuclei in the lattice are in vibrational and rotational motion, which creates a complex magnetic field magnetic field caused by motion of nuclei within the lattice is called the

lattice field lattice field has many components Some components will be equal in frequency and phase to the

Larmor frequency of the nuclei of interest These components of the lattice field can interact with nuclei in the

higher energy state cause them to lose energy (returning to the lower state) energy that a nucleus loses increases the amount of vibration and

rotation within the lattice (resulting in a tiny rise in the temperature of the sample).

• relaxation time, T1 (the average lifetime of nuclei in the higher energy state) is dependant on the magnetogyric ratio of the nucleus and the mobility of the lattice As mobility increases, the vibrational and rotational frequencies

increase, making it more likely for a component of the lattice field to be able to interact with excited nuclei

at extremely high mobilities, the probability of a component of the lattice field being able to interact with excited nuclei decreases.

11-10

Spin-Lattice Relaxtion

11-11

Spin Lattice Relaxation

11-12

Spin-Lattice Relaxation

11-13

Name Pulse Sequence signal evolution vs T1

Inversion Recovery (IRFT)

                        D1-180-tau-90-Acq{D1+Acq>5*T1}

M(tau)/M0= 1-2*exp(-tau/T1)

Progressive Saturation (PSFT)

                 (preceded by dummy pulses) - D1-90-Acq{tau=D1+Acq}

M(tau)/M0= 1-exp(-tau/T1)

Saturating Comb(Mainly useful in solid)require: T2*<<T1

                               {n*90-t}-tau-90-Acqt: pulse spacing during Comb. :T2*< t <T1

tau: delay for magnetization recovery

M(tau)/M0= 1-exp(-tau/T1)

11-14

Spin-Spin Relaxation

• Spin - spin relaxation describes the interaction between neighboring nuclei with identical precessional frequencies differing magnetic quantum states

• nuclei can exchange quantum states a nucleus in the lower energy level will be excited

the excited nucleus relaxes to the lower energy state

no net change in the populations of the energy states the average lifetime of a nucleus in the excited

state will decrease• can result in line-broadening• T2

11-15

Spin-Spin Relaxation

11-16

Chemical Shift

• A molecule may contain multiple protons that exist in unique electronic environments.

• Therefore not all protons are shielded to the same extent.

• Resonance differences in protons are very small (ppm).

• Measure differences in resonance energy relative to a reference.

• Tetramethylsilane (CH3)4Si (TMS) provides highly shielded reference (set to 0ppm).

Nuclear Shielding

• Nuclei are shielded by electrons.

• Induced field associated with orbiting electrons.

• Require stronger magnetic field than H0.

• Increased shielding requires greater applied field strength to achieve resonance.

Chemical Shift (, ppm) =Observed chemical shift from TMS (Hz)

Sptectrometer frequencey (MHz) = ppm

11-17

NMR Spectra

• Hypothetical NMR spectra.• Shows TMS reference.• Chemical shifts (, ppm) given relative to TMS

A b s o r b a n c e

0123456789101112

Increasing magnetic field strength

, ppm

TMS

CH

HH

TMS as reference is set to 0 ppm

Representative peak,3 equivalent protons

Increased sheilding of nuclei

11-18

Chemically Equivalent

• Protons in the same environment will have the same chemical shift.

• Protons in different environments have different chemical shifts.

• Protons with the same chemical shift are referred to as chemically equivalent.

• Integrated area of peak is proportional to the number of protons.

H

H

H

H

H

HC

C

H

H

H

H

H

H

H

C

H

H

H

H

H

H

H

C

C

H

H

H

H

C

H

H H

H

11-19

Sample Spectra

• The first spectra is that of a symmetric molecule, all protons are equivalent.

• Second spectra is that of a molecule containing two types of protons.

• Correlation chart for proton chemical shift

A b s o r b a n c e

0123456789101112 , ppm

TMS

C

C

H

H

H

H

H

H

A b s o r b a n c e0123456789101112 , ppm

TMS

H

CH

H

HHH

H

H

11-20

Type of Proton StructureChemical Shift, ppm

Cyclopropane C3H6 0.2

Primary R-CH3 0.9

Secondary R2-CH2 1.3

Tertiary R3-C-H 1.5

Vinylic C=C-H 4.6-5.9

Acetylenictriple bond,CC-

H2-3

Aromatic Ar-H 6-8.5

Benzylic Ar-C-H 2.2-3

Allylic C=C-CH3 1.7

Fluorides H-C-F 4-4.5

Chlorides H-C-Cl 3-4

Bromides H-C-Br 2.5-4

Iodides H-C-I 2-4

Alcohols H-C-OH 3.4-4

Ethers H-C-OR 3.3-4

Esters RCOO-C-H 3.7-4.1

Esters H-C-COOR 2-2.2

Acids H-C-COOH 2-2.6

Carbonyl Compounds

H-C-C=O 2-2.7

Aldehydic R-(H-)C=O 9-10

Hydroxylic R-C-OH 1-5.5

Phenolic Ar-OH 4-12

Enolic C=C-OH 15-17

Carboxylic RCOOH 10.5-12

Amino RNH2 1-5

11-21

11-22

11-23

Nuclear Shielding/Deshielding

• Valence electron density can shield nucleus from applied field.

• Electronegative substituents can draw elecron density away.

• Results in deshielding.• Anisotropy: -electrons and

induced magnetic field.• Results in shielding and

deshielding zones.

H

H0

O HH

A n i s o t r o p y

CH3F CH3OCH3 (CH3)3N CH3CH3

(ppm) 4.3 3.2 2.2 0.9

CHCl3 CH2Cl2 CH3Cl

(ppm) 7.3 5.4 3.1

E l e c t r o n e g a t i v e

S u b s t i t u e n t s

11-24

Spin-spin Splitting and n+1 Rule

• Each type of proton “senses” protons on adjacent carbon atoms.

• Spin state of nearby protons contributes to the proton evironment and apparent magnetic field.

• General rule is that the signal is split into n+1 peaks. n = number of equivalent neighboring protons.

• Spacing between component peaks referred to as coupling constant (J).

• J coupling is representative of the degree to which protons interact.

• J usually 0-18Hz

n = 2, tripletn = 1, doublet

-1/2+1/2 0+1 -1

n = 3, quartet

-1/2+1/2

-1 1/2+1 1/2

Numbers in Italics refer to net spin

Splitting

n = 0, singlet

Cl C

Ha

Cl

C

Hb

Hb

Cl Cl C

Ha

Cl

C

Hb

Hb

Cl

equivalent protons behave as a group

Two types of protons in 1,1,2-trichloroethane

11-25

Splitting patterns

1

1 1

11 2

11 3 3

11 4 46

11 5 10 510

Pascal's Triangle

n = 2, tripletn = 1, doublet

-1/2+1/2 0+1 -1

n = 3, quartet

-1/2+1/2

-1 1/2+1 1/2

Numbers in Italics refer to net spin

Splitting

n = 0, singlet

11-26

1,1,2-trichloroethane

• NMR spectrum for 1,1,2-trichloroethane• Hb proton signal split into doublet• Ha proton signal split into triplet• J couplings are the same for Ha and Hb signals• Ha integral is 1/2 that of Hb

A b s o r b a n c e

012345678 , ppm

TMS

Cl C

Ha

Cl

C

Hb

Hb

Cl

J J

J

Hb

Ha

11-27

Magnetic Equivalence vs. Chemical Equivalence

• NMR differentiates between nuclei based on environment.

• In constrained systems, two protons on the same C-atom can be in different environments.

• These protons can demonstrate spin-spin splitting.

Ha

HbH3C

Br

Br

H3C

X

HcHa

Hb

11-28

Higher Field Strengths

• At higher field strengths differences in energy between spin states is increases.

• Improved signal resolution.

• Coupling constants are independent of field strength.

A b s o r b a n c e

012345678 , ppm

A b s o r b a n c e

01234 , ppm

TMS

TMS

60 MHz

100 MHz

60 MHz

100 MHz

Chemical Shift (, ppm) =Observed chemical shift from TMS (Hz)

Sptectrometer frequencey (MHz) = ppm

11-29

Carbon-13 NMR

• ~1.08% of C atoms are the 13C isotope.

• Do not usually see C-C spin-spin interactions.

• Can see coupling between C and attached H’s.

• Magnetic moment of 13C is low.• Resonances of 13C nuclei are ~6000

fold weaker than 1H resonances.• Therefore most useful information

is chemical shift.• Covers a range of 0-200ppm.

A b s o r b a n c e

0 , ppm

TMS

OH2C

H2C

O

CH3

20406080100120140160180

Undecoupled

Decoupled from protons

O CH2 CH3

H2C C

O12

34

5

6

1

2,63,5

4

C

O

Ethyl phenylacetate

11-30

Proton Decoupled

• Proton coupling can provide information about number of protons.

• Often useful to decouple protons.

• Irradiate sample with broad spectrum of frequencies.

• Substituents on C can enhance of reduce signal.

• Protons enhance the 13C signal.

A b s o r b a n c e

0 , ppm

TMS

OH2C

H2C

O

CH3

20406080100120140160180

Undecoupled

Decoupled from protons

O CH2 CH3

H2C C

O12

34

5

6

1

2,63,5

4

C

O

11-31

Spectrometer

• Magnet Shim and lock

• Sample probe Coils and receiver

11-32

NMR imaging

• NMR imaging with a trivalent lanthanide tracer has been applied to the study of transport and sorption in ion exchange resins

• The tracer, Gd3+, is a highly effective NMR contrast agent and an excellent chemical analog for trivalent actinidesTrivalent lanthanide7 electrons in f orbital

• Results from these studies can be used to improve modeling and prediction

11-33

NMR Imaging• Advantages:

2 and 3-D analysis of heterogeneous granular structureInherently non-invasive probe of spatial structureNear real-time analysis of static and dynamic processesFlexibility to adapt experimental methods to various

sample types and configurations• Limitations:

Paramagnetic and/or ferromagnetic impurities can create artifacts and image distortions

Low porosity can lead to long experiment times (proton NMR)

11-34

Ion-Specific Exchange Resins

• Developed to partition similar inorganic species from waste streams Cooperation with French partners in CNAM,

ENSCP

• Synthetic organic structures with phenolic functional groups

• Resorcinol formaldehyde (RF) resins were used in these experiments (11.5 meq/g dry)

• RF resins were crushed, sieved (80-200 ASTN mesh), washed, and conditioned to Na+ form

11-35

NMR Flow Systemshowing evacuation, de-aeration, and over- pressurization systems

NoldDe-aerator

stepper motorw/ hydraulicpiston for

pressure control

vacuum pump

11-36

Oxford 3T NMR Magnet with 60 G/cm Imaging Gradient Set

11-37

• T1 Relaxation: spin-lattice or longitudinal relaxation of the spin system

measured using an inversion recovery sequence where, Mz(t) = Mo[ 1 - 2 (exp(-t /T1)) ]

NMR Basics - spin relaxation

Inversion Recovery Curve -T1 DeterminationDI Water vs. 0.1 mM Gd Solution

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

10.

00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

Time (sec)

Rel

ativ

e M

agn

etiz

atio

n-M

z(t)

o

T1 for 0.1mM Gd in Sand is 400ms

T1 for DI Water in Sand is 1730ms

DI Water

0.1 mM Gd Solution

11-38

TT11 Weighting Experiment Weighting Experiment - - Inversion RecoveryInversion Recovery

5mm tube of H5mm tube of H22O surrounded by 0.1mM Gd solution in sandO surrounded by 0.1mM Gd solution in sand

Water signal suppressed

Gd Signal IntensityWeighted

11-39

Gd Sorption with Phenolic Resin and Sand8mm diameter by 15mm long sample saturated w/ 1.0 mM Gd

sand/resin interface

11-40

Image 1: water saturated sample Image 2: 55ml of 1.0mM Gd in Image 3: 80ml of Gd in

Image 4: 110ml of Gd in Image 5: 160ml of Gd in Image 6: 200ml of Gd in

Flow direction

NMR Imaging Studies of 2-D Flow1.0 mM Gd into homogenized RF resin and sand sample

Fingering Flow Phenomenon

0.8

1.25cm

cm

11-41

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 100 200 300 400 500 600 700 800 900 1000

Total Volume Into Column (ml)

[Gd

] ou

t / [

Gd]

in

End of Gd Flow

#6

#4

#3

#5

Resin Column data

11-42

Gadolinium Complexation with Phenolic RF Resin8mm diameter by 15mm long resin sample saturated with 1.0 mM Gd solution

Hot Spots Showing Gd Sorption Sites

Cool Spots Showing Voids and Low Sorption Sites