Transcript 2 Theory of NMR - coercingmolecules

05- NMR Instrumentation
1. Overview of the JEOL LA400
2. Superconducting magnet
3. The magnetic field and
homogeneity
4. Field frequency lock
5. Pulse program
6. Decoupler
7. Radiofrequency generator
8. Probe
9. Amplifier, detector and receiver
10. Analog to digital converter
11. Sensitivity and Resolution
12. Peak shape
Introduction
•
Compared with other spectroscopic methods, NMR
provides the richest amount of structural information.
However, in order to properly obtain and process complex
information, it is necessary to use sophisticated techniques.
• NMR is, in many ways, the most difficult spectroscopic
technique to learn. To a great degree, the quality of the
NMR result is dependent on the skill and know-how of the
operator.
•
If one is doing a routine analysis of known compounds,
one can run the NMR as a “black box”. However, if one
needs to determine a structure, or wishes to use NMR to its
fullest advantage, then one should master its operation.
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1. Overview of the NMR instrument
Main features of the JEOL LA400:
• 9.4 T SCM, long hold magnet; 54 mm bore
• 2-channels: high frequency and low frequency
• tunable frequencies
• temp control: -70 ~ +150 °C
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Tunable frequencies in the high and low frequency range.

13C
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1. Overview of the NMR instrument
1. Pulse program
2. RF oscillator / carrier freq. (r)
3. Amplifier (A)
4. RF pulse generator
5. NMR excitation
6. NMR signal (0) to pre-amp. (PA)
7. Amplified signal
8. Reference frequency
9. RF receiver
10. Digitization and processing
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2. The Superconducting Magnet
• At higher fields (>5 T), SCMs give
superior stability and are actually less
expensive to operate. The
superconducting coils are immersed in
liquid helium (boiling point: -269 oC;
4 K) in an inner dewar, which is
surrounded by an outer dewar of liquid
nitrogen (bp: -196 oC; 77 K). Both
liquid cryogens require periodic
refilling. Once the SCM is filled and
started, it should run continuously for
many years unless the
superconductivity quenches.
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Magnex, 9.4 T SCM
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2. The Superconducting Magnet
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3. Magnetic Field Homogeneity
•
The magnetic field must be
very homogeneous over the
observed volume of the sample
in order that all of the spins
within the observation volume
have the same magnetic field. A
lack of homogeneity means that
the various spins experience
different magnetic fields.
• For high resolution NMR, the
tolerance of homogeneity is 1
part in 109, or 1 ppb.
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The SCM coil is
made up of special
alloys containing Cu,
and other metals.
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3. Magnetic Field Homogeneity
•
The SCM coils do not produce a sufficiently homogeneous
magnetic field. In order to improve the homogeneity, a small
secondary magnetic field is added using shim coils*. For
liquid samples, the NMR tube is rotated rapidly in order to
average out the inhomogeneities in the perpendicular
direction.
A "shim" is a thin piece or wedge of thin tapered pieces of material,
usually wood or metal, to make fine adjustments on the fit of separate
parts which need to be joined together.
In the making of bells, shims are used for fine-tuning the resonance.
Just like the shims used for bells, NMR *shim coils enable fine
adjustments of the magnetic field gradient. Whenever a new sample is
inserted into the probe, there are slight changes in the magnetic field
homogeneity due to the NMR tube, the solvent, sample, etc.
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3. Magnetic Field Homogeneity
• SCMs can have from 13 to over 20 shim coils depending on
the instrument design.
• The coils whose field is aligned along the vertical axis of
the magnet are called the Z-gradient coils, designated, Z1,
Z2, Z3, etc. The Z0 coil functions as a fine magnetic field
adjustment.
• The field in the horizontal plane is adjusted via the higher
order corrections designated as: X, Y (first order); XZ, YZ,
XY, and X2-Y2 (second order); XZ2 and YZ2 (third order)
and others.
• Because the shim adjustments interact, shimming is an
iterative process.
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4. Field/Frequency Lock
The preparations for measuring an NMR spectrum are similar in
some ways to the tuning of a radio to the desired radio station.
• First, one must tune into the desired radio station;
analogously, the experimenter must locate the signal of the
target nucleus, a process which is appropriately called tuning.
• Second, the radio signal should be locked in. Generally, the
radio station operator does this for you by seeing to it that the
frequency of transmission does not drift; some modern digital
radios, nevertheless, have a radio signal locking feedback
device. Analogously, the NMR spectrometer must be locked
onto the desired nucleus. The NMR lock must be very
accurate and precise if we are to have high resolution.
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4. Field/Frequency Lock
There are two aspects to maintaining a good lock: a stable
magnet and an efficient lock system. For SCMs at 400 MHz, the
magnetic field stability (drift) is <8 Hz/hr. This stability is better
than 1 part in over 40 x 106, but is insufficient for the
requirements of a long NMR experiment.
• A field/frequency lock fixes the reference lock signal using a
deuterated (2H) solvent so that the lock signal is derived from
the sample itself (internal lock). The alternative is to use an
external lock which places a substance containing usually 2H
or 19F at a close distance away from the sample.
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4. Field/Frequency Lock
A feedback is used in the
field/frequency lock. The
receiver is equipped with a
phase sensitive detector which is
set on the dispersion mode
signal of the lock signal.
An output voltage of zero indicates the precise resonance
condition of the reference. A positive or negative drift in the
magnetic field is detected as a positive or negative voltage,
respectively. This voltage is converted into a correcting signal
on magnetic field via the Z0 shim coil.
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5. Pulse Program
The pulse program is the software interface which the
operator uses to set instructions for the NMR. This is what
the operator uses to perform the NMR experiment. The
operator must some knowledge of NMR to be able to set the
parameters appropriately. The most important parameters that
have to be set are the following:
• type of NMR experiment (pulse sequence)
• pulse width (pulse angle)
• number of accumulations
• resolution (Hz/point)
• spectral width
• pulse delay
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5. Pulse Program
The excitation of the nuclear spins is accomplished using both
pulses and continuous irradiation of RF energy. The pulses
programs are stored in the NMR software and these
instructions are sent to the transmitter for implementation.
In order to implement an NMR experiment, one must have the
appropriate pulse program, NMR hardware, and processing
software.
•
Many pulse programs were designed to overcome
imperfections of NMR hardware.
•
Some pulse programs require certain types of NMR
hardware for them to work.
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One controls the NMR experiment by selecting the
appropriate pulse program and parameters.
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5. Pulse program
 The pulse angle depends on the pulse width which is the
duration of the pulse, designated tp. The pulse width is
empirically determined and depends on the particular sample.
The pulse width results in the tipping of the magnetization
vector by a certain pulse angle. The most common pulse
angles are: 45o, 90o, 180o, and 270o (- 90o).
 M can be tipped down to the –z direction with a 180o
resulting in a spin population inversion. This corresponds to
an excited energy condition where the equilibrium
populations of the spin states N and N are inverted.
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5. Pulse Program
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
The same pulse angle can be achieved by means of a hard
pulse or a long, weak pulse (a soft pulse). A typical hard pulse
lasts for several s, while a soft pulse can last for several ms.
Read pulses are usually hard pulses, while double resonance
pulses are usually soft pulses.
 The pulse phase is the axis from which the NMR pulse is
implemented. Pulses can be applied along the x’or y’ axes.
 The detector is placed along the y’-axis and the pulse sequence
is designed so that the final position of the magnetization vector
is along this axis. For this purpose, many pulse sequences must
incorporate a read pulse which places the vector along the y’axis immediately prior to the collection of the FID. This pulse
which is usually applied along the x’-axis.
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
In a multipulse experiment, time delays, tD, are inserted
between pulses or other elements of the sequence to allow
the spins to evolve. If the time delay is variable and
incremented, this is referred to as t1 in a 2-dimensional NMR
experiment. If the time delay is fixed, this is usually a
mixing time.

The acquisition time, AQT, refers to the time allocated for
the collection of the FID. This normally lasts from about half
a second to a few seconds.
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 A pulse delay, PD, of about 3-5 times T1 is added after
the acquisition time before repeating the pulse sequence.
This is necessary to allow the spin system to return to its
equilibrium value so that M = Mo (this also means that
Mx = My = 0). This requirement gives rise to practical
difficulties for nuclei with very long T1 relaxation times,
such as quaternary carbons which can have T1s of up to
100 seconds! One possible solution is to use smaller pulse
angles so that relaxation time is shorter.
 Note: T1  T2
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Illustration of two simple pulse programs. The basic
components of a pulse program are: the pulse, delay time,
acquisition time, relaxation delay, and decoupler.
t PW
1-Dimensional
NMR: 1 H
Observe:
1H
preparation
Irradiate:
AQT
tD
1H
t PW
1-Dimensional
NMR: 13 C
Observe:
13 C
preparation
Irradiate:
AQT
tD
1H
IRR
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 - zero filling

 - spectral width
 - no. of accum
 - T1 and 
-
 - 0
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6. Decoupler
All nuclei with I  0 have magnetic properties and therefore
interact with other magnetically-active nuclei (“spin-spin
coupling”). The NMR spectrum contains information
regarding all of these interactions. Depending on what one
needs, this can be good or bad. The technique of removing
contributions from coupling is called decoupling.
• One of the earliest innovations in NMR was the
introduction of multiple irradiation in CW 1H NMR. This
allowed the experimenter to specifically irradiate a specific
proton frequency while taking the entire spectrum. If the
coupling information being removed is from the same
nucleus, the technique is called homonuclear decoupling.
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6. Decoupler
•
If the nuclei being decoupled and observed are different, the
technique is heteronuclear decoupling. There are several ways
of carrying out heteronuclear decoupling: broadband
decoupling (the standard 13C NMR), selective heteronuclear
decoupling, off-resonance decoupling, and gated decoupling.
•
Broadband decoupling requires the application of decoupling
energy over a wide band. For example, in a 1H-decoupled 13C
spectrum in a 400 MHz machine, decoupling has to be applied
over at least 4,000 Hz. The most common technique used is
noise modulation wherein the decoupler energy is distributed
uniformly over the 1H range by random modulation.
•
Today, there is a many sophisticated and clever ways of
implementing decoupling and multiple irradiation.
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7. Radiofrequency Generator
•
In order to carry out the NMR experiment, three
independent RF fields are needed: for observation, for
secondary irradiation (e.g., for decoupling), and for
locking. These three frequencies may or may not be set for
the same nucleus.
Pulse program
•
The three frequencies are
independently synthesized from
the RF generator (master
oscillator). The switch combines
the pulse program with the RF
frequencies.
RF generator
Switch
Amplifier
Receiver
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Pulse generator
Probe
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7. Radiofrequency Generator
•
The power that is needed depends on several factors: 1. the
bandwidth (in Hz) that needs to be excited; 2. the desired
pulse angle; 3. the probe characteristics; and 4. sample.
•
In pulse NMR, the RF field, B1, should be uniform over the
entire bandwidth of the nuclei under observation. Since the
RF field tapers off at the ends, the RF field should be set for a
wider range of frequencies.
•
The strength of the RF field, B1, generated is proportional to
the square of the power used: B1  w2. If one wishes to
double the field strength, the power must be increased by four
times. This, unfortunately, generates more heat.
• A typical performance specification for a 1H 90° pulse at 400
MHz is 15 s at 50 W power.
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8. Probe
The sample is placed in an NMR tube which is nested in the
probe. The probe houses the coils and associated RF electronics.
The probe is designed to carry out the following functions: 1. to
hold the spinning NMR tube in a precise manner; 2. to efficiently
transmit the RF energy, B1, to the sample (pulse); 3. to pick up
the resulting NMR signal for transmission to the receiver
(observe); 4. to transmit energy for decoupling; and 5. to provide
for an efficient third frequency for locking. In recent years, there
has been much effort put into optimizing probe performance.
•
There are specific probes for different NMR tubes, most
commonly 5 mm and 10 mm.
• NMR probes are designed to operate at temperatures ranging
from -100 to +150 oC for variable temperature experiments.
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8. Probe
• Since there are two channels
(HF and LF), the probe should
have two coils. The coils can
be arranged in two ways:
• standard probe: LF coil
inside and HF coil outside
• inverse probe: HF coil
inside and LF coil outside
• Probe innovations:
• Pulsed field gradient
(PFG) probe
• Microcoil probes.
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9. Amplifier, Detector and Receiver
•
The receiver must amplify the signal linearly without
distortion and added noise, from an initial magnitude of
nanovolts to microvolts, to tens of volts required by the
analogue-to-digital converter (ADC). Noise can arise from
various sources such as the transmitter and receiver themselves,
the NMR coils (which are actually radio antennas which can
vibrate), and external noise (e.g., lightning, fluctuations or
spikes in the line current, etc.).
• In radio technology, the function of the detector is to subtract
the carrier frequency from the signal. In the case of a NMR, the
detector has to subtract the carrier frequency, o (which is at the
Larmor frequency of 400 MHz in the case of 1H at 9.4 T), so
that we will observe only  (which has values in Hz).
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9. Amplifier, Detector and Receiver
•
When setting up an NMR experiment, the position of the
reference frequency, o, has to be set. There are two choices:
at the upper edge of the frequency range of interest or in the
middle. The first option requires a wider bandwidth which
collects more noise than necessary.
• All modern NMR spectrometers implement the second
option of placing the reference frequency in the middle of the
spectral range. This has two important advantages: first, there
is less noise by virtue of the narrower range; and second, this
requires a lower digitization speed. However, this has to
address the problem of distinguishing the signals which occur
on either side of the reference frequency (quadrature
detection).
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10. Analog to Digital Converter (ADC)
The ADC enables the conversion of electrical signals (volts at
small time intervals) into numerical form. There is an inherent
difficulty in adequately representing a continuous analogue signal
in terms of discrete numbers.
•
The conversion of the analogue FID into digital form is
implemented by converting the voltage into binary form (y-axis)
as discrete points over time (x-axis). There are two important
characteristics of the ADC: the number of bits used in the binary
representation (the word length) and the digitization rate. The
first word length determines the digitizer resolution and dynamic
range, while the digitization rate determines the maximum
spectral width and digital resolution.
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10. Analog to Digital Converter (ADC)
•
As already mentioned, we can make the analysis of the signal
easier by subtracting the reference frequency from the total
signal. So instead of processing frequencies of about 400 MHz,
we need to only process signals generally in the fractions of Hz
up to the 4-5 kHz range (a 10 ppm spectral range is equivalent to
4000 Hz). In order to cover a spectral width of 4000 Hz, the
digitization rate of our ADC has to be at least: (2 x 4000 Hz) = 8
kHz, or a dwell time of 1.25 x 10-4 sec. The factor of 2 arises
from the requirement of the Nyquist theory.
•
In order to properly record a waveform, the Nyquist theory tells
us that at least two data points are needed for each cycle. Failure
to do so results in the improper recording of frequencies leading
to frequency dependent anomalies known as aliasing or folding.
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10. Analog to Digital Converter (ADC)
• In this example, sampling is carried out at 100 s intervals (10
kHz). This gives a Nyquist frequency of 5 kHz. Since the two
waves have frequencies of 4.5 kHz (solid line) and 1.2 kHz
(dotted line), then this sampling rate is adequate and we can
represent the two frequencies correctly.
Sampling rate:
10 kHz
Solid line:
4.5 kHz
Dotted line:
1.2 KHz
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10. Analog to Digital Converter (ADC)
• In this example, we have two signals: 7 kHz and 3 kHz. If we
sample with a frequency of 10 kHz, the 3 kHz signal will be
correctly detected, but the 7 kHz signal will be aliased or
folded.
• To correctly record the FID, our ADC has to run at a
minimum of twice the highest frequency signal present.
Sampling rate:
10 kHz
Solid line:
3 kHz
Dotted line:
7 KHz
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10. Analog to Digital Converter (ADC)
•
The requirement for digitization rate for 1H work is easy to meet
since the spectral range of the 1H nucleus is narrow and therefore
requires a relatively slow ADC rate. In comparison, a 230 ppm
spectral width for 13C at 100 MHz requires a digitization rate of
at least 2 x 23000 Hz = 46 kHz.
• Standard ADCs are usually rated for at least 100 kHz which
means a maximum spectral width of 50 kHz.
•
The second aspect important characteristic of the ADC is the
number of bits it uses in the binary representation. The number of
bits of data used limits both the sensitivity of the NMR
experiment. The sensitivity is related to the dynamic range which
is defined as the ratio of the biggest to the smallest signal.
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10. Analog to Digital Converter (ADC)
•
In practice, the maximum voltage range that is outputted in
the FID is adjusted to the highest value of the digitizer; and
the smallest signal that is recorded is that which gives a
response of 1-bit. This is what is sometimes referred to as the
digitizer resolution (not to be confused with the digital
resolution).
• A sufficiently large digitizer is needed in order that all
signals are measured. An inadequate digitizer can result in the
nondetection of some peaks. In samples which contain both
very large and very small signals (for example a dilute
solution in an aqueous solvent), very small signals may be
present but not be detected because of the limitation of the
dynamic range.
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10. Analog to Digital Converter (ADC)
•
NMR instruments are available with an ADC resolution of 16
bits. (The ADC resolution, however, is adjustable for each NMR
run.) A 16-bit digitizer, covers the range 0 to 1111111111111111
(=216) in binary. Since one digit is reserved for the sign of the
signal (+/-), the actual range is from 0 to 216 - 1. With a 16-bit
ADC, the largest signal will be 32767 and the smallest is 1.
• The digital resolution (given in Hz/point) refers to the accuracy
with which the frequency of the signal can be presented in
digitized form. According to theory, the resolution is also related
to the length of time that we allow to record the FID; this is
called the acquisition time. In general, the longer the acquisition
time, the better our resolution:
digital resolution, Hz = (1 / acquisition time, s)
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11. Sensitivity and Resolution
•
“Sensitivity” is one of the most important goals of a
spectroscopic technique. Mathematically, sensitivity is
measured using the dimensionless signal-to-noise ratio (S/N):
(sensitivity, S/N) = 2.5 Sht / Npp
where
2.5 is a factor obtained from statistics
Sht is the signal height
Npp is the peak-to-peak height at the noise level
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11. Sensitivity and Resolution
• The key goal of all spectroscopic methods is to obtain
the highest resolution and sensitivity. However,
there are theoretical and practical aspects that need to
be considered. The resolution set by the NMR
parameters is given as:
Resolution = (frequency range / no. of points), ( Hz / point )
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11. Sensitivity and Resolution
•
Some NMR parameters favor both resolution and
sensitivity: magnetic field strength and homogeneity.
• Others parameters affect resolution and sensitivity in
reciprocal ways: spectral width, acquisition time and ADC.
In these cases, the operator needs to decide how much
resolution and sensitivity are needed and then select the
parameters accordingly. The trade-off between sensitivity
and resolution is thus:
(sensitivity, S/N)  1 / (resolution, Hz / point)
•
Other phenomena, such as nuclear relaxation and kinetics,
also affect sensitivity and resolution.
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12. Peak Shape
Comparison between normalized
Lorentzian (solid) and Gaussian
(dashed) distributions. Note that the
area under both curves is 1.
1J
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= 209 Hz
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NMR parameters that affect resolution and sensitivity.
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spectral width, SW
wider SW decreases resolution
wider SW lengthens acq time and
decreases sensitivity for same
experiment time
05-NMR Instrumentation (Dayrit)
43
Overview of JEOL LA 400 NMR operation
Network
Data
Storage and
Processing
Sequence
Part of the NMR
1. Load sample, Tune probe
2. Lock
3. Shim, spin
4. NMR experiment proper
 Probe
 Field/frequency lock
 Magnetic field homogeneity
 Pulse program
5. Data processing
[RF generator, transmitter and
amplifier decoupler, detector and
receiver, ADC]
 Host computer