Nuclear Magnetic Resonance (NMR) Spectroscopy

1
Nuclear Magnetic Resonance (NMR) Spectroscopy
Dr. Vincent J. Storhaug
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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
develop the energy states (produce a separation
of the energy states) necessary for the
absorption to occur.
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Development of Energy States of Nuclei in an
Applied Magnetic Field
Spin ½ Nucleus Bar Magnet
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Development of Energy States of Nuclei in an
Applied Magnetic Field
Spin ½ Nucleus Bar Magnet
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Populations of the Energy States of Hydrogen
Nuclei (Spin ½ Nuclei) in a Magnetic Field
Ea
Without an applied magnetic field, there is no
division of energy states to discuss.
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Development of Energy States of Nuclei in an
Applied Magnetic Field
The nuclei have a property of spin,
characterized by
p angular momentum quantized in units of
h/(2p) I spin quantum number will be in integer
or half-integer values
This angular momentum is directly related to the
magnetic dipole moment, µ, by
? magnetogyric ratio, dependent on the type of
nucleus
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Development of Energy States of Nuclei in an
Applied Magnetic Field
There will be 2I1 discrete energy states, as
indicated by
???
I
I-1
I-2
-I
This value is called the magnetic quantum state,
mI.
The simplest situation, therefore is a system of
two energy states, i.e. I ½.
The value of I for 1H, 13C, 19F, and 31P is ½, so
we have
½
-½
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Magnetic Properties of the Four Most Commonly
Observed Nuclei
Magnetogyric Ratio (radian T-1 s-1)
Relative Sensitivity
Absorption Frequency (MHz)
Nucleus
1H 13C 19F 31P
2.6752 x 108 6.7283 x 107 2.5181 x 108 1.0841
x 108
1.00 0.016 0.83 0.066
400 100.6 376.5 162.1
All of these nuclei have spin I
½! http//www.chem.tamu.edu/services/NMR/periodi
c/index.shtml
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Development of Energy States of Nuclei in an
Applied Magnetic Field
Potential energy, E, and the energy difference
between two given states
0
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Transition of Nucleus from One Energy State to
Another
Planck relationship, between ?E and an applied
radio frequency, ?0 is
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Relationship Between Resonance Frequency and the
Applied Field Strength
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Boltzmann Distribution of Nuclei Among the Energy
Levels
Nj the number or nuclei occupying the higher
energy state N0 the number or nuclei occupying
the lower (ground) energy state
Since (for NMR active nuclei) when you apply a
magnetic field, Bo , a nonzero difference between
the energy states develops, ?E, then we know that
Nj will always be smaller than N0.
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Boltzmann Distribution of Nuclei Among the Energy
Levels
Experimentally, we can do only two things in
order to increase the difference in populations
of the ground and excited states 1. We can
increase the strength of the applied field,
B0. 2. We can decrease the absolute temperature,
T.
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Example Calculation of the Distribution of Nuclei
Among the Energy Levels
1H NMR, calculate the ratio Nj/N0, for an NMR
system where the magnet has a field of 4.69 T,
and the temperature is 20 ºC.
i.e. The populations differ by less than 0.004!
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Basics of Fourier Transform NMR Relying on
Nuclear Precession
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NMR Relying on Radio Frequenciesand Nuclear
Precession
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Continuous Wave (CW) NMR
B0
B0
?0
?
Absorption
µZ
µ
µZ
µ
?
?
Emission
?
?0
m1/2
m-1/2
Circularly Polarized Radiation
µZ magnetic field vector (magnetic vector from
the rotating frame of reference) µ spin axis of
the nucleus ? angle between the magnetic field
vector and the spin axis of the particle
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Continuous Wave (CW) NMR
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Continuous Wave (CW) NMR

• Low magnetic field strength needed (advantage
  AND disadvantage)
• Low sensitivity, and limited to a single sweep
  of the spectral window
• (If you have a small amount of material, you
  are simply out of luck)
• Low resolution (1 Hz linewidth FWHM - is
  considered great resolution for CW)
• Limited mostly to 1H NMR ONLY. 13C NMR not
  possible due to decreased sensitivity
• (and single sweep)
• No computer is necessary, direct plotting of
  spectrum, but also no way to digitally
• save spectrum.

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Basics of Fourier Transform NMR Relying on
Nuclear Precession
where ?0 is the angular velocity of the
precession, in radians/second
Experimentally, we need to convert this angular
velocity to its corresponding frequency in the
electromagnetic spectrum
where ?0 is now in millions of rotations per
second units, or commonly, Megahertz (MHz). ?0
is referred to as the Larmor Frequency.
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The Fourier Transform Pulsed NMR Technique
M0
B0
B0
Laboratory (Static) Frame of Reference
Rotating Frame of Reference
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Where the Quantum Explanation Ends, and the
Classical One Takes Over
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Basics of Fourier Transform NMR Relying on
Nuclear Precession
z
Rotating Frame of Reference
M0
y
x
B0
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The Fourier Transform Pulsed NMR Technique
time
Delay
Pulse
Delay
Acquisition
time
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The Fourier Transform Pulsed NMR
Technique(Rotating Frame of Reference)
time
90º
M0
RF
M0
B1
B0
B0
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The Fourier Transform Pulsed NMR
Technique(Rotating Frame of Reference)
a
RF
M0
Mz
My
B1
B1
B0
B0
a angle of rotation in radians ? magnetogyric
ratio (radians T-1 s-1) B1 induced magnetic field
(T) t pulse width (s)
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The Fourier Transform Pulsed NMR
Technique(Rotating Frame of Reference)
time
M0
B0
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The Fourier Transform Pulsed NMR
Technique(Rotating Frame of Reference)
0
time
M0
M0
M0
M0
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Basics of Fourier Transform NMR Measuring the
Precession Frequency
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Relaxation Process in NMR
Spin-Lattice Relaxation, T1 The absorbed energy
is lost through vibrational and rotational motion
to the magnetic components of the lattice of
the sample. Problem The temperature of the
sample can rise over time. Spin-Lattice
relaxation processes cause an exponential decay
of the excited state population. The more viscous
a sample is, or the more restricted the motion of
a molecule is, the larger the T1. Spin-Lattice
relaxation is the slower of the relaxation
processes. Spin-Spin Relaxation, T2 Several
processes are lumped under this term, but one
of the predominant techniques is spin diffusion,
a process requiring neighboring nuclei to have
the same precession rates, but different magnetic
quantum numbers. Another cause is a disruption in
the homogeneity of the magnetic field through the
sample caused by the sample itself. (e.g.
formation of dimers, trimers, etc. that change
the relaxation rates of nuclei.) Spin-Lattice
relaxation is the faster of the relaxation
processes. Thus, T2 is the primary influence on
line broadening in the spectrum.
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Spin-Spin Relaxation, T2
Mxy
time
z
y
x
time
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Longitudinal Spin-Lattice Relaxation, T1
Mxy
time
My
Mz
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Longitudinal Spin-Lattice Relaxation, T1
The time constant, T1,describes how MZ returns to
its equilibrium value. The equation governing
this behavior as a function of the time t after
its displacement is T1 is therefore
defined as the time required to change the Z
component of magnetization by a factor of e. If
the net magnetization is placed along the -Z
axis (i.e. pw 180º), it will gradually return
to its equilibrium position along the Z axis
at a rate governed by T1. The equation governing
this behavior as a function of the time t after
its displacement is
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Relaxation of Mxy During Fourier Transform NMR
Responses Due to T1 AND T2
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Basics of Fourier Transform NMR The Free
Induction Decay
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Signal to Noise Improvement
With digital summations of FIDs (or rather,
transients),
where n is the total number of scans acquired.
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Signal to Noise Improvement Practical
Considerations

1. Running a 13C NMR spectrum.
2. Not limited so much in the amount of sample, but
   by the solubility of the compound in the
   available solvent (deuterated CDCl3)
3. Ran the sample for 4 hours, and it looks like

In order to increase the S/N by a factor of 2,
this would need to run for 16 hours. In order to
increase the S/N by a factor of 4, this would
need to run for 64 hours (almost 3 days).
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CW vs FT NMR
Continuous Wave
Fourier Transform

• Samples are run neat
• Less expensive, no deuterated
• solvents are necessary
• Larger quantities of sample are
• needed (gram)
• Limited primarily to 1H NMR (dedicated)
• Slow acquisition, have to sweep the
• frequencies
• Signal to Noise limited in what can be
• seen in a single sweep

• Samples are run diluted
• More expensive, MOST of the sample
• actually being a deuterated solvent
• Very small quantities (ltlt mg) are
• possible
• Interchangeable probes, multiple nuclei.
• All frequencies are measured in a rapid scan
• (milliseconds)
• Theoretically, the Signal to Noise is limited
• only by the time available to acquire the
• spectrum