1. NUCLEAR MAGNETIC RESONANCE
Dr. Nermin Salah
6th Lecture

2. Objectives Properties of the nucleus Nuclear spin
Nuclear magnetic moments
The nucleus in a magnetic field
Precession of nuclei in a field
The “Resonance” Phenomenon
NMR techniques
Continuous wave
Pulsed or Fourier transform (FT-NMR)
Instrumentation

3. NMR Spectroscopy
NMR spectroscopy is a form of absorption spectrometry.
Most absorption techniques (e.g. – Ultraviolet-Visible and Infrared) involve the electrons… in the case of NMR, it is the nucleus of the atom which determines the response.
An applied (magnetic) field is necessary to for the absorption to occur.

4. Spectral Properties, Application and Interactions of Electromagnetic Radiation
Energy
Wave
Number V
Wavelength λ
Frequency υ
Type
Radiation
Type
spectroscopy
Type
Quantum Transition
Kcal/mol
Electron volts, eV
cm-1 cm Hz
9.4 x 107
4.9 x 106
3.3 x 1010
3 x 10-11
1021
9.4 x 103
4.9 x 102
3.3 x 106
3 x 10-7
1017
9.4 x 101
4.9 x 100
3.3 x 104
3 x 10-5
1015
9.4 x 10-1
4.9 x 10-2
3.3 x 102
3 x 10-3
1013
9.4 x 10-3
4.9 x 10-4
3.3 x 100
3 x 10-1
1011
9.4 x 10-7
4.9 x 10-8
3.3 x 10-4
3 x 103
107
Gamma ray
Gamma ray emission
Nuclear
X-ray absorption, emission
Electronic (inner shell)
X-ray
Ultra violet
UV absorption
Electronic (outer shell)
Visible
Infrared
IR absorption
Molecular vibration
Molecular rotation
Micro-wave
Microwave absorption
Magnetically induced spin states
Nuclear magnetic resonance
Radio 4

5. Nuclear Spin
Nuclear spin angular momentum is a quantized property of the nucleus in each atom, it is assigned based on the properties of neutrons and protons.
The nuclear spin angular momentum of each atom is represented by a nuclear spin quantum number (I).
All nuclei with even mass numbers have I = 0,1,2…
All nuclei with odd mass numbers have I = 1/2, 3/2...
NMR is possible with all nuclei except I = 0, but I = 1/2 has simplest physics.

6. SPIN QUANTUM NUMBERS OF SOME COMMON NUCLEI
The most abundant isotopes of C and O do not have spin.
Element 1H 2H 12C 13C 14N 16O 19F
Nuclear Spin
Quantum No 1/ / /2
( I )
No. of Spin
States
In many atoms, these spins are paired against each other, such that the nucleus of the atom has no overall spin such as 12C, 16O, 32S.
However, in some atoms (such as 1H, 13C, 19F, 31P ) the nucleus does possess an overall spin (odd no. of protons or neutrons [odd mass number or odd atomic number]).
The nucleus with spin quantum no. I  0, can assume (2I +1) possible orientations (states).
A nucleus with spin 1/2 will have 2 possible orientations (i.e. two possible energy states) described by magnetic quantum number mI=+1/2 and mI=-1/2
Elements with either odd number of protons or neutrons (odd mass number or odd atomic number) have the property of nuclear “spin”.
The number of spin states is 2I + 1,
where I is the spin quantum number.

7. NUCLEAR SPIN STATES – MAGNETIC MOMENT
A spinning, charged nucleus creates a magnetic field.
Thus, the spinning charged nucleus is characterized by a certain magnetic moment, .
Since a nucleus is a charged particle in motion, it will develop a magnetic field, they behave in a similar fashion to a simple, tiny bar magnet. In the absence of a magnetic field, these are randomly oriented.
When a magnetic field is applied the nuclei line up parallel to the applied field, either spin aligned or spin opposed.
Always consider hydrogen nuclei for simplicity, the whole nuclei contains only one proton.
More nuclei align with the applied magnetic field as it is the lower energy spin state .

8. Behavior of spinning protons with external magnetic field
(-spin state)
(β-spin state)

9. THE PROTON Although interest is increasing in other nuclei,
particularly C-13, the hydrogen nucleus (proton)
is studied most frequently, and we will devote
our attention to the proton at first.
Now on, the acronym “NMR” is generally assumed to mean 1H-NMR (Proton Magnetic Resonance)

10. NUCLEAR SPIN STATES - HYDROGEN NUCLEUSm +
Clockwise spin
Anticlockwise spin
Hydrogen Nucleus
One Proton
I = 1/2
Two states (2I+1 = 2)
mI= + ½ & mI= - ½
-spin state, mI= + ½
-Spin state, mI= - ½
(magnetic quantum number)
TWO SPIN STATES
two possible orientations (two possible energy states)

11. In a strong magnetic field (Bo) the two spin states differ in energy
THE NUCLEUS IN A MAGNETIC FIELD
When nuclei are exposed to external magnetic field of strength B0, their spins line up parallel to the applied field, either spin aligned (-spin state) or spin opposed (-spin state) to the external field. Bo
aligned
opposing N S
Nuclear Spin Energy Levels
+ ½
 ½
higher in energy
lower in energy
-spin state
-spin state
Imagine as if in a magnetic field : E0-E1
In a strong magnetic field (Bo) the two spin states differ in energy

12. THE “RESONANCE” PHENOMENON
absorption of energy by
spinning nuclei in a magnetic field

13. A Quantum Description of NMR
When sample is subjected to a pulse of radiation whose energy corresponds to the difference in energy (E) between the -spin state and the -spin state, the nuclei in the -spin state flip their spin and are promoted to the -spin state.
The term resonance refers to the spin flipping back and forth between the - and -spin states in response to rf radiations. Bo
DE = hn DE
quantized
Radiofrequency
Applied
Field
Aligned
Opposed
+ ½
 ½
-spin state
-spin state

14. POPULATION AND SIGNAL STRENGTH
The strength of the NMR signal depends on the Population Difference of the two spin states
In external magnetic field, the  and  states will be populated (occupied by nuclei) and the population difference is dependent on the nuclear species under observation.
The difference in population is very small with only about 20 out of 1 million in excess in the lower energy state.
The NMR signal depends essentially on a such a small difference.
Ground state
Resonance
Absorption
of rf
spin flip
Excited state
For a net positive signal, there must be an excess of spins in the lower state.

15. THE ENERGY SEPARATION DEPENDS ON Bo
The stronger the external magnetic field, the higher the energy of the excited state, the higher the energy required to flip the nuclear spin.
- 1/2
-spin state DE
Bo = 0 all nuclei have the same energy
+ 1/2
-spin state Bo
increasing magnetic field strength

16. Energy difference between the two state
Energy of spinning nuclei
The energy of the nucleus in these two states (orientations) is given by:
Energy of -state (spin aligned)
Energy of -state (spin opposed)
Energy difference between the two state
Absorption of electromagnetic radiation of frequency  that correspond to in energy to E

17. THE LARMOR EQUATION g is a constant which is different for
gyromagnetic
ratio g
Frequency of
the incoming
radiation that
will cause a
transition
strength of the
magnetic field
g is a constant which is different for
each atomic nucleus (H, C, N, etc)

18. Rf Frequencies for different nuclei

19. “Where the Quantum Explanation Ends, and the Classical One Takes Over”
To understand the absorption process , and in particular the measurement of absorption, a classical picture of the behavior of a charged particle in a magnetic field is helpful.
Since the nuclei are spinning rapidly around its axis, the magnetic field applied to the axis of rotation forces the nuclei to move in a circular path.
The rotational axis of the nuclei precess around the vector representing the applied magnetic field.
The nuclei is precessing with angular velocity ω or better say with frequency of precession (Larmor frequency)
Same derived from quantum mechanics

20. If nradiation = wprecession
Nuclei precess at frequency  (Larmor precession frequency) when placed in a strong magnetic field.
  B0  
Energy will be
absorbed and
the spin will
invert
If nradiation = wprecession w hn
NUCLEAR
MAGNETIC
RESONANCE
Applied
Field Bo
RADIOFREQUENCY
MHz
NMR S

21. CLASSICAL INSTRUMENTATION
Before 1970
Continuous wave NMR : The sample is held in a strong magnetic field, and the frequency of the source is slowly scanned or vice versa, the source frequency is held constant, and the magnetic field is scanned.
Disadvantages
The magnitude of the energy changes involved in NMR spectroscopy are small
Slow scanning
Fourier – Transform NMR were introduced in 1970.
Low sensitivity
Hard to improve S/N ratio

22. A Simplified 60 MHz NMR Spectrometerhn
RF (60 MHz)
Oscillator RF
Detector
absorption
signal
Recorder
Radiation source,
its magnetic field is what matters
Receiver
MAGNET
MAGNET N S
~ 1.41 Tesla
(+/-) a few ppm
Probe
For protons (1H), affected by magnetic field of 1.41 Tesla (~14000 gauss), the needed frequency was found to be 60 MHz

23. MODERN INSTRUMENTATION
PULSED FOURIER TRANSFORM
TECHNOLOGY
FT-NMR
requires a computer

24. Interval between pulses
PULSED OR FOURIER TRANSFORM (FT-NMR) SPECTROMETERS
Nuclei in a very strong magnetic field (constant strength) are subjected periodically to very brief pulses of intense radio-frequency radiation.
Pulse duration or pulse width
Interval between pulses
Pulse train
Each pulse is actually a packet of RF radiation

25. The NMR Experiment WHAT HAPPEN BEFORE IRRADIATION
Before irradiation, the nuclei in both spin states are precessing with the Larmor frequency, but they are completely out of phase, i.e., randomly oriented around the z axis.
The net nuclear magnetization M0 is aligned statically along the z axis (M0=Mz, Mxy=0)
The NMR Experiment

26. WHAT HAPPEN DURING IRRADIATION
Excitation is produced by a second magnetic field, B1, which oscillate at the appropriate radio-frequency. This field is induced from alternating current in a coil (source of radiation) wound perpendicular to B0.
When irradiation begins:
Under the effect of B1, the net magnetization M0 is displaced from equilibrium and is flipped toward the xy plane . The tip angle or the flip angle, , is determined by the power and duration of the electromagnetic irradiation (time for which B1 is turned on). Z z  x
Mxy y B0 Mo y x B1 Y y x wo X
 deg pulse
90 deg pulse

27. WHAT HAPPEN AFTER IRRADIATION CEASES
After irradiation ceases, B1 turns off after the pulse, the magnetic moment M0 must now rotate in clockwise direction back to presses around the z axis.
This motion gives rise to a signal (current) that can be detected by the same coil (along the x axis) that is used to produce the original pulse.
As relaxation proceeds, this signal decreases exponentially and approach zero as the magnetic moment reaches the z axis. (Note that the coil acts as a receiver coil or detector that can sense only the magnetic field on the xy plane).
This time domain signal is called the free induction decay (FID signal)
FID: free of the influence of radio-frequency field, induced current in the coil and decaying back to equilibrium. z y
Mxy x Mo
90y pulse
relaxation B1
B1=0 B0
Transmitter (source)
receiver (detector)
Relaxation: Loss of excess energy in the system to surrounding (lattice) as heat

28. FREE INDUCTION DECAY SIGNALz x
Mxy y Mo
Free Induction Decay
(FID) - One frequency
90y pulse
relaxation

29. The Pulse FT NMR Experiment
equilibration
90º pulse
detection of signals
Experiment
(t)
Data
Analysis
Fourier
Transform
Time domain (t)

30. The Composite FID is Transformed into a classical NMR Spectrum
“frequency domain” spectrum

31. COMPARISON OF
CW AND FT TECHNIQUES

32. CONTINUOUS WAVE (CW) METHOD
THE OLDER, CLASSICAL METHOD
The magnetic field is “scanned” from a low field
strength to a higher field strength while a constant
beam of radiofrequency (continuous wave) is
supplied at a fixed frequency (say 60 MHz).
Using this method, it requires several minutes to plot
an NMR spectrum.
SLOW, HIGH NOISE LEVEL

33. PULSED FOURIER TRANSFORM (FT) METHOD
FAST
LOW NOISE
THE NEWER COMPUTER-BASED METHOD
Most protons relax (decay) from their excited states
very quickly (within a second).
The excitation pulse, the data collection (FID), and
the computer-driven Fourier Transform (FT) take
only a few seconds.
The pulse and data collection cycles may be repeated
every few seconds.
Many repetitions can be performed in a
very short time, leading to improved signal to noise ratio.

34. NMR instrumentation N S Magnet - Normally Superconducting.Bo B1
Detector
Frequency
Generator
Recorder
Magnet
Magnet - Normally Superconducting.
Frequency generator Creates an alternating current that induces B1.
Detector
Recorder 34

35. NMR spectrometer in organic labs

36. The cost of NMR A superconducting magnet A Strong magnetic field
Stable, homogenous field up to 21 Tesla (900MHz)
Requires cooling to absolute zero (liquid Nitrogen or Helium)
A Strong magnetic field
requires special infrastructure to avoid any possible interference.
NMR is a very expensive technique.

37. Is such a spectrum worth millions?
Brainstorming
Using a magnetic field of 2.4 Tesla, for an organic sample containing H- protons, absorbance of ν= 100 MHZ will occur.
A spectrum with one signal indicating the presence of H- protons in the compound.
Is such a spectrum worth millions?
100 MHz

38. Resources and references
Textbook: Principles of Instrumental Analysis, Skoog, Holler, Nieman
Recommended further reading:
“Principles of instrumental analysis, 5th ed. by Skoog, Holler, Nieman” Chapter 19.
Extra resources are available on the intranet.
Relevant web sites