Transcript nuclear spin states

NUCLEAR MAGNETIC RESONANCE
Dr. Nermin Salah
6th Lecture
16-10-2011
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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
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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.
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Spectral Properties, Application and Interactions of
Electromagnetic Radiation
Energy
Kcal/mol
9.4 x 107
9.4 x 103
9.4 x 101
Electron
volts,
eV
4.9 x 106
4.9 x 102
4.9 x 100
Wave
Number V
cm-1
Wavelength
λ
cm
3.3 x
1010
3 x 10-11
3.3 x 106
3 x 10-7
3.3 x 104
3 x 10-5
Frequency
υ
Hz
1021
Type
Radiation
Type
spectroscopy
Type
Quantum Transition
Gamma
ray
Gamma ray
emission
Nuclear
1017
X-ray
1015
Ultra
violet
X-ray
absorption,
emission
Electronic
(inner shell)
UV absorption
Electronic
(outer shell)
Visible
IR absorption
9.4 x 10-1
4.9 x 10-2
3.3 x 102
3 x 10-3
1013
Infrared
9.4 x 10-3
4.9 x 10-4
3.3 x 100
3 x 10-1
1011
Microwave
Microwave
absorption
Radio
Nuclear
magnetic
resonance
9.4 x 10-7
4.9 x 10-8
3.3 x 10-4
3 x 103
107
Molecular
vibration
Molecular
rotation
Magnetically
induced spin
states
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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.
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SPIN QUANTUM NUMBERS OF SOME COMMON NUCLEI
The most abundant isotopes of C and O do not have spin.
Element
Nuclear Spin
Quantum No
1H
2H
12C
13C
14N
16O
19F
1/2
1
0
1/2
1
0
1/2
2
3
0
2
3
0
2
(I)
No. of Spin
States
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.
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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.
 More nuclei align with the applied magnetic field as it is the lower
energy spin state .
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Behavior of spinning protons with
external magnetic field
(-spin state)
(β-spin state)
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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)
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NUCLEAR SPIN STATES - HYDROGEN NUCLEUS

Hydrogen Nucleus
One Proton
I = 1/2
Two states (2I+1 = 2)
+
+
Clockwise spin
-spin state, mI= + ½

m I= + ½ & m I= - ½
Anticlockwise spin
-Spin state, mI= - ½
(magnetic quantum number)
TWO SPIN STATES
two possible orientations (two possible energy states)
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THE NUCLEUS IN A MAGNETIC FIELD
When nuclei are exposed to
Nuclear Spin Energy Levels
external magnetic field of
strength B0, their spins line
N
up parallel to the applied
½
field, either spin aligned (-
higher
in
energy
-spin state
opposing
spin state) or spin opposed
(-spin state) to the external
field.
Bo
+½
-spin state
S
lower
in
energy
aligned
In a strong magnetic field (Bo) the
two spin states differ in energy11
THE “RESONANCE” PHENOMENON
absorption of energy by
spinning nuclei in a magnetic field
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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.
Opposed
½
½
-spin state
E
+½
-spin state
Applied
Field
Bo
Aligned
E = hn
Radiofrequency
quantized
+
½
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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
spin flip
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
Excited state
Absorption
of rf
For a net positive signal, there must be
an excess of spins in the lower state.
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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
E
Bo = 0 all nuclei have
the same energy
+ 1/2
-spin state
Bo
increasing magnetic field strength
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Energy of spinning nuclei
The energy of the nucleus in these two states (orientations) is given by:
E
mh
B0
2
Energy of -state
(spin aligned)
Energy of -state
(spin opposed)
 ( 12 )h
E 1  
B0
2
2
h
E  1   B0
2
4
Energy difference
between the two
state
 ( 12 )h
E 1  
B0
2
2
h
E 1 
B0
2
4
h
h
h
E 
B0  ( 
B0 ) 
B0
4
4
2
Absorption of electromagnetic radiation of frequency n that
correspond to in energy to E
h
E  h n 
B0
2
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THE LARMOR EQUATION
gyromagnetic
ratio 
Frequency of
the incoming
radiation that
will cause a
transition

E  n  B0
2
strength of the
magnetic field
 is a constant which is different for
each atomic nucleus (H, C, N, etc)
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Rf Frequencies for different nuclei
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“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)

n B
2
0
Same n derived from
quantum mechanics
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N
Nuclei precess at
frequency w (Larmor
Energy will be
absorbed and
the spin will
invert
w
precession frequency)
when placed in a
strong magnetic
field.
If
n
radiation
= wprecession
w  B0  
NUCLEAR
MAGNETIC
RESONANCE
hn
Applied
Field
RADIOFREQUENCY
80 - 900 MHz
Bo
S
NMR
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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
Low sensitivity
Slow scanning
Hard to improve
S/N ratio
Fourier – Transform NMR were introduced in 1970.
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A Simplified 60 MHz
NMR Spectrometer
RF (60 MHz)
Oscillator
hn
Radiation source,
its magnetic field is what matters
absorption
signal
RF
Detector
Recorder
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),
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the needed frequency was found to be 60 MHz
MODERN INSTRUMENTATION
PULSED FOURIER TRANSFORM
TECHNOLOGY
FT-NMR
requires a computer
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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 radiofrequency radiation.
Interval between
pulses
Pulse duration
or pulse width
Pulse train
Each pulse is actually a
packet of RF radiation
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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)
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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

B0
Mo
xy
yx
B1
wo
Y
yx
y
x
Mxy
X
 deg pulse
90 deg pulse
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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
z
Mo
B0
B0
y
B1
x
90y pulse
relaxation
Transmitter (source)
y
Mxy
B1=0
x
Relaxation: Loss of
excess energy in
the system to
surrounding (lattice)
as heat
receiver (detector)
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FREE INDUCTION DECAY SIGNAL
z
z
Mo
x
90y pulse
x
relaxation
y
y
Mxy
Free Induction Decay
(FID) - One frequency
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The Pulse FT NMR Experiment
90º pulse
Experiment
(t)
equilibration
detection of signals
Fourier
Transform
Data
Analysis
Time domain (t)
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The Composite FID is Transformed into a
classical NMR Spectrum
O
CH2 C CH3
“frequency domain” spectrum
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COMPARISON OF
CW AND FT TECHNIQUES
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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
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PULSED FOURIER TRANSFORM
(FT) METHOD
FAST
THE NEWER COMPUTER-BASED METHOD
LOW NOISE
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.
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NMR instrumentation
Bo
N
S
Magnet
B1
Recorder
Frequency
Generator
Detector
1. Magnet - Normally Superconducting.
2. Frequency generator Creates an alternating current that induces B1.
3. Detector
4. Recorder
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NMR spectrometer in organic labs
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The cost of NMR
A superconducting magnet
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.
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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
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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
http://www.chemguide.co.uk/analysismenu.html
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