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Chem 355 10 Lecture 34 Nuclear Magnetic Resonance. Option I: Final 60%; MT 25%; Assign. 15% Option II: Final 75%; MT 10%; Assign. 15% Option II: 1 alternate question more heavily weighted on early material. .

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slide1

Chem 355 10 Lecture 34

Nuclear Magnetic Resonance

slide2

Option I: Final 60%; MT 25%; Assign. 15% Option II: Final 75%; MT 10%; Assign. 15%

Option II: 1 alternate question more heavily weighted on early material.

slide3

Many nuclei possess spin angular momentum. For a nucleus with spin I:

  • 1. There is an angular momentum:
  • There is a component of the angular momentum mI around a particular axis in which mI = I, I-1, … -I
  • If I > 0 there is a magnetic moment with a constant magnitude and orientations determined by the value of mI.

There are 2I + 1 orientations of the angular momentum vector so for nuclei with I = ½ such as 1H, 19F, 13C or 31P there are 2 orientations with mI = +1(↑) denoted a and mI = (↓) denoted b.

slide4

Many nuclei possess spin angular momentum. For a nucleus with spin I:

  • 1. There is an angular momentum:
  • There is a component of the angular momentum mI around a particular axis in which mI = I, I-1, … -I
  • If I > 0 there is a magnetic moment with a constant magnitude and orientations determined by the value of mI.

There are 2I + 1 orientations of the angular momentum vector so for nuclei with I = ½ such as 1H, 19F, 13C or 31P there are 2 orientations with mI = +1(↑) denoted a and mI = (↓) denoted b.

slide5

Many nuclei possess spin angular momentum. For a nucleus with spin I:

  • 1. There is an angular momentum:
  • There is a component of the angular momentum mI around a particular axis in which mI = I, I-1, … -I
  • If I > 0 there is a magnetic moment with a constant magnitude with orientations determined by the value of mI.

There are 2I + 1 orientations of the angular momentum vector so for nuclei with I = ½ such as 1H, 19F, 13C or 31P there are 2 orientations with mI = +1(↑) denoted a and mI = (↓) denoted b.

slide6

Many nuclei possess spin angular momentum. For a nucleus with spin I:

  • 1. There is an angular momentum:
  • There is a component of the angular momentum mI around a particular axis in which mI = I, I-1, … -I
  • If I > 0 there is a magnetic moment with a constant magnitude with orientations determined by the value of mI.

There are 2I + 1 orientations of the angular momentum vector so for nuclei with I = ½ such as 1H, 19F, 13C or 31P there are 2 orientations with mI = +1/2(↑) denoted a and mI = (↓) denoted b.

slide7

Nuclear Spin Properties

Nuclide Natural abundance/% Spin g-values

1n 1/2 -3.826 1H 99.98 1/2 5.586 2H 0.02 1 0.857 13C 1.11 1/2 1.405 14N 99.64 1 0.404 19F 100 1/2 5.257 31P 100 1/2 2.263

slide8

The common nuclei that are examined in organic molecules are 1H (protons) and 13C. Protons and 19F are easier to examine in that their I = 1/2 nuclei have large magnetic moments.

slide9

The nuclear magnetic moment is denoted m the same as that for an electric dipole moment. The component of the nuclear magnetic moment along the z-axis is given by:

where is the magnetogyric ratio. The magnetic moment can be expressed in terms of the nuclear g-factor and the nuclear magneton bN as:

where: = 5.051x10-27 JT-1with mP the proton mass.

Positive values of g are associated with a magnetic moment parallel to the spin while negative values indicate that the magnetic moment and spin are antiparallel.

slide10

The nuclear magnetic moment is denoted m the same as that for an electric dipole moment. The component of the nuclear magnetic moment along the z-axis is given by:

where is the magnetogyric ratio. The magnetic moment can be expressed in terms of the nuclear g-factor and the nuclear magneton bN as:

where: = 5.051x10-27 JT-1with mP the proton mass.

Positive values of g are associated with a magnetic moment parallel to the spin while negative values indicate that the magnetic moment and spin are antiparallel.

slide11

The nuclear magnetic moment is denoted m the same as that for an electric dipole moment. The component of the nuclear magnetic moment along the z-axis is given by:

where is the magnetogyric ratio. The magnetic moment can be expressed in terms of the nuclear g-factor and the nuclear magneton bN as:

where: = 5.051x10-27 JT-1 with mP the proton mass.

Positive values of g are associated with a magnetic moment parallel to the spin while negative values indicate that the magnetic moment and spin are antiparallel.

slide12

The nuclear magnetic moment is denoted m the same as that for an electric dipole moment. The component of the nuclear magnetic moment along the z-axis is given by:

where is the magnetogyric ratio. The magnetic moment can be expressed in terms of the nuclear g-factor and the nuclear magneton bN as:

where: = 5.051x10-27 JT-1 with mP the proton mass.

Positive values of g are associated with a magnetic moment parallel to the spin while negative values indicate that the magnetic moment and spin are antiparallel.

slide13

In a magnetic field B the 2I + 1 orientations of the nucleus have energies:

These energies are often expressed in terms of the Larmor frequency: nL

where:

The stronger the magnetic field, the higher the Larmor frequency. A field of 12T corresponds to a Larmor frequency of about 500 MHz for protons. The energy separation of the two states of spin-1/2 nuclei is:

slide14

In a magnetic field B the 2I + 1 orientations of the nucleus have energies:

These energies are often expressed in terms of the Larmor frequency: nL

where:

The stronger the magnetic field, the higher the Larmor frequency. A field of 12T corresponds to a Larmor frequency of about 500 MHz for protons. The energy separation of the two states of spin-1/2 nuclei is:

slide15

In a magnetic field B the 2I + 1 orientations of the nucleus have energies:

These energies are often expressed in terms of the Larmor frequency: nL

where:

The stronger the magnetic field, the higher the Larmor frequency. A field of 12T corresponds to a Larmor frequency of about 500 MHz for protons. The energy separation of the two states of spin-1/2 nuclei is:

slide16

In a magnetic field B the 2I + 1 orientations of the nucleus have energies:

These energies are often expressed in terms of the Larmor frequency: nL

where:

The stronger the magnetic field, the higher the Larmor frequency. A field of 12T corresponds to a Larmor frequency of about 500 MHz for protons. The energy separation of the two states of spin-1/2 nuclei is:

slide17

The combination of the angular momentum due to the spin and the magnetic field results, like a spinning top or draedal in precession about the magnetic field direction.

The precession occurs at the Larmor frequency nL.

slide18

b

mI = -1/2

mI = +1/2

a

field off field on

slide19

The population of the upper state b is close to that of the lower state due to the small DE relative to kT.

It follows that:

The population difference is proportional to B.

slide20

The population of the upper state b is close to that of the lower state due to the small DE relative to kT.

It follows that:

The population difference is proportional to B.

slide21

In the presence of radiation at a frequency n = nL, the system is in resonance

It follows that:

The population difference is proportional to B.

slide22

With almost 1/2 of the spins in the sample aligned in either direction in the sample, but with a slight excess in the direction of the B-field, there is a bulk magnetization that can be represented at a vector Mz aligned in the field direction:

slide23

In the presence of radiation in which the frequency of the oscillating magnetic vector in the radiation n = nL, the Larmor frequency, there is a resonance resulting in absorption as spins are excited to the b state, with a resulting decrease in the magnitude of Mz.

With the large number of spins aligned in either direction and the low frequencies involved the behavior of bulk magnetization vector can be viewed as essentially behaving according to classical physics.

Resonance, or the absorption condition, can, and has been arrived at, either by holding the external field fixed and varying the radiation frequency or, as with ESR by varying the magnetic field until the DE and therefore vL, reaches n, the fixed radiation frequency of the spectrometer.

slide24

In the presence of radiation in which the frequency of the oscillating magnetic vector in the radiation n = nL, the Larmor frequency, there is a resonance resulting in absorption as spins are excited to the b state, with a resulting decrease in the magnitude of Mz.

With the large number of spins aligned in either direction and the low frequencies involved the behavior of bulk magnetization vector can be viewed as essentially behaving according to classical physics.

Resonance, or the absorption condition, can, and has been arrived at, either by holding the external field fixed and varying the radiation frequency or, as with ESR by varying the magnetic field until the DE and therefore vL, reaches n, the fixed radiation frequency of the spectrometer.

slide25

In the presence of radiation in which the frequency of the oscillating magnetic vector in the radiation n = nL, the Larmor frequency, there is a resonance resulting in absorption as spins are excited to the b state, with a resulting decrease in the magnitude of Mz.

With the large number of spins aligned in either direction and the low frequencies involved the behavior of bulk magnetization vector can be viewed as essentially behaving according to classical physics.

Resonance, or the absorption condition, can, and has been arrived at, either by holding the external field fixed and varying the radiation frequency or, as with ESR by varying the magnetic field until the DE and therefore vL, reaches n, the fixed radiation frequency of the spectrometer.

slide26

In the earlier spectrometers the standard approach was, as with ESR, to sweep B until resonance was observed at the fixed frequency of the instrument, usually 60 MHz.

slide27

In the earlier spectrometers the standard approach was, as with ESR, to sweep B until resonance was observed at the fixed frequency of the instrument, usually 60 MHz.

Changes in technology in the 70’s led to the development of large magnets, as well as the use of frequency sweep rather than Bo-field sweep to detect the signal. Fourier Transform methodology was introduced as the process of detection.

slide28

In the earlier spectrometers the standard approach was, as with ESR, to sweep Bo until resonance was observed at the fixed frequency of the instrument, usually 60 MHz.

Changes in technology in the 70’s led to the development of large magnets, as well as the use of frequency sweep rather than Bo-field sweep to detect the signal. Fourier Transform methodology was introduced as the process of detection.

NMR spectrometers operating at 100, 220, 500 and 800 MHz are now in use. The large magnetic fields used to generate these fields are at liquid helium temperatures, or are superconducting.

slide29

The large Bo-fields result in a larger DE, increasing the population difference and resulting sensitivity. In addition the chemical shift differences that will be examined shortly are spread further apart, enhancing the resolution.

slide30

The large Bo-fields result in a larger DE, increasing the population difference and resulting sensitivity. In addition the chemical shift differences that will be examined shortly are spread further apart, enhancing the resolution.

In order to assure homogeneity in the Bo field the sample that is placed between the poles of the magnet is spun at a frequency of 15 Hz so that the spins in all parts of the sample experience the same averaged field.

slide31

The large Bo-fields result in a larger DE, increasing the population difference and resulting sensitivity. In addition the chemical shift differences that will be examined shortly are spread further apart, enhancing the resolution.

In order to assure homogeneity in the Bo field the sample that is placed between the poles of the magnet is spun at a frequency of 15 Hz so that the spins in all parts of the sample experience the same averaged field.

slide32

The radiation that induces transitions in the spin states in the sample is oriented with the oscillating magnetic vector B1in the xy-plane. The magnetic spin vectors precessing about the z-axis are induced to align with the B1 vector so that the bulk magnetization vector is directed into the xy-plane, but rotating at the Larmor frequency:

slide33

The radiation that induces transitions in the spin states in the sample is oriented with the oscillating magnetic vector B1in the xy-plane. The magnetic spin vectors precessing about the z-axis are induced to align with the B1 vector so that the bulk magnetization vector is directed into the xy-plane, but rotating at the Larmor frequency:

slide35

With the B1 field in x-direction, the signal is detected along the y-direction.

In standard frequency-sweep spectrometry absorption or emission is detected as the frequency of the radiation is swept over a range of frequencies generating a spectrum.

slide36

With the B1 field in x-direction, the signal is detected in y-direction.

In standard frequency-sweep spectrometry absorption or emission is detected as the frequency of the radiation is swept over a range of frequencies generating a spectrum.

In the Fourier-transform method of detection the sample is irradiated with an excitation pulse containing all frequencies in the same pulse. The response in the signal following the pulse is followed with time and is referred to as the FID or free-induction decay.

slide37

With the B1 field in x-direction, the signal is detected in y-direction.

In standard frequency-sweep spectrometry absorption or emission is detected as the frequency of the radiation is swept over a range of frequencies generating a spectrum.

In the Fourier-transform method of detection the sample is irradiated with an excitation pulse containing all frequencies in the same pulse. The response in the signal following the pulse is followed with time and is referred to as the FID or free-induction decay.

The various frequency components in the sample manifest themselves in the decaying signal, and their individual frequencies and intensities are recovered from the decaying signal through a Fourier transformation.

slide39

The pulsed NMR signal:

In the presence of the Bo field (constant external field), there is a slight excess of spins in the magnetic field direction, so that the net magnetization vector Mo (Mz) is pointing in the Bo- field direction:

slide40

The pulsed NMR signal:

In the presence of the Bo field (constant external field), there is a slight excess of spins in the magnetic field direction, so that the net magnetization vector Mo (Mz) is pointing in the Bo- field direction:

The magnetic moments are precessing about the z-axis at the Larmor frequency.

slide41

A short pulse (mseconds) of radiation at the Larmor frequency is aplied with the oscillating magnetic component B1 in x-direction in the xy-plane. While the radiation might appear to be monochromatic, due to the short duration of the pulse it spans a range of frequencies (uncertainty principle).

As a result:

the magnitude of Mois reduced due to the increase in the population of b spins with magnetic moments opposing the Bo field.

The magnetization vector is tipped into the xy-plane due to the precession of Moabout B1 and is focused along e.g. the rotating y-direction.

slide42

A short pulse (mseconds) of radiation at the Larmor frequency is aplied with the oscillating magnetic component B1 in x-direction in the xy-plane. While the radiation might appear to be monochromatic, due to the short duration of the pulse it spans a range of frequencies (uncertainty principle).

As a result:

the magnitude of Mois reduced due to the increase in the population of b spins with magnetic moments opposing the Bo field.

The magnetization vector is tipped into the xy-plane due to the precession of Moabout B1 and is focused along e.g. the rotating y-direction.

slide43

A short pulse (mseconds) of radiation at the larmor frequency is aplied with the oscillating magnetic component B1 in x-direction in the xy-plane. While the radiation might appear to be monochromatic, due to the short duration of the pulse it spans a range of frequencies (uncertainty principle).

As a result:

the magnitude of Mois reduced due to the increase in the population of b spins with magnetic moments opposing the Bo field.

The magnetization vector is tipped into the xy-plane due to the precession of Moabout B1 and is focused along e.g. the rotating y-direction.

slide44

The radiation that induces transitions in the spin states in the sample is oriented with the oscillating magnetic vector B1in the xy-plane. The magnetic spin vectors precessing about the z-axis are induced to align with the B1 vector so that the bulk magnetization vector is directed into the xy-plane, but rotating at the Larmor frequency:

slide45

The focusing of the magnetic moments so that they are tilted specifically in the y-direction* requires what is denoted as a 90o pulse. It refocuses Mo from the z to the y axis. The pulse that will bring about precession of Mo about B1 through 90o is determined by the intensity of the B1 field and its duration.

Just as:

*The y-direction represents a coordinate in a rotating frame . which itself is rotating about the Z-axis at the larmor . frequency.

slide46

The focusing of the magnetic moments so that they are tilted specifically in the y-direction* requires what is denoted as a 90o pulse. It refocuses Mo from the z to the y axis. The pulse that will bring about precession of Mo about B1 through 90o is determined by the intensity of the B1 field and its duration.

Just as:

*The y-direction represents a coordinate in a rotating frame . which itself is rotating about the Z-axis at the larmor . frequency.

slide47

The focusing of the magnetic moments so that they are tilted specifically in the y-direction* requires what is denoted as a 90o pulse. It refocuses Mo from the z to the y axis. The pulse that will bring about precession of Mo about B1 through 90o is determined by the intensity of the B1 field and its duration.

Just as:

*The y-direction represents a coordinate in a rotating frame . which itself is rotating about the Z-axis at the larmor . frequency.

slide48

The focusing of the magnetic moments so that they are tilted specifically in the y-direction* requires what is denoted as a 90o pulse. It refocuses Mo from the z to the y axis. The pulse that will bring about precession of Mo about B1 through 90o is determined by the intensity of the B1 field and its duration.

Just as:

*The y-direction represents a coordinate in a rotating frame . which itself is rotating about the Z-axis at the Larmor . frequency.

slide49

With gP = 2.675x108 s-1T-1 for a proton, and given B1 = 1.57x10-4 T:

Given the particular intensity of the B1 field, a 90o pulse should be 10 msec in duration.

slide50

With gP = 2.675x108 s-1T-1 for a proton, and given B1 = 1.57x10-4 T:

Given the particular intensity of the B1 field, a 90o pulse should be 10 msec in duration.

slide51

With gP = 2.675x108 s-1T-1 for a proton, and given B1 = 1.57x10-4 T:

Given the particular intensity of the B1 field, a 90o pulse should be 10 msec in duration.

slide52

With gP = 2.675x108 s-1T-1 for a proton, and given B1 = 1.57x10-4 T:

Given the particular intensity of the B1 field, a 90o pulse should be 10 msec in duration.

slide53

Following the pulse the magnetization vector Mx,yrotates in the x-y plane and is detected as an oscillating signal. The oscillating signal decays with time as the individual magnetic moments fan out and as a result Mx,y decays to zero. The FID decays contains components:

i) with differing frequencies corresponding to protons in . distinct environment in a molecule. . ii) apparently, equivalent spins precess at slightly differing . frequencies due to inhomogeneities in the sample and . differences that arise from spin-spin interactions.

slide54

Following the pulse the magnetization vector Mx,yrotates in the x-y plane and is detected as an oscillating signal. The oscillating signal decays with time as the individual magnetic moments fan out and as a result Mx,y decays to zero. The FID decays contains components:

i) with differing frequencies corresponding to protons in . distinct environment in a molecule. . ii) apparently, equivalent spins precess at slightly differing . frequencies due to inhomogeneities in the sample and . differences that arise from spin-spin interactions.

slide55

There are 2 relaxation process in spin resonance spectroscopy. These are referred to as: 1. transverse-, or spin-lattice relaxation time; T1 and, longitudinal- or spin-spin relaxation time; T2.

The T1 relaxation process denotes the process in which the excited spin states undergo non-radiative relaxation back to the equilibrium distribution of spin states. It is analogous to the excited-state lifetimes that appear in fluorescence and phosphorescence decays in electronic excited states.

The T2 relaxation process represents the decay of the net magnetization vector in the x-y plane. This process dominates the decay of the FID and is therefore involved in the detection of the signal.

T2 relaxation can be << than T1 so that following the decay of FID, the spin states have not returned to equilibrium

slide56

There are 2 relaxation process in spin resonance spectroscopy. These are referred to as: 1. transverse-, or spin-lattice relaxation time; T1 and, longitudinal- or spin-spin relaxation time; T2.

The T1 relaxation process denotes the process in which the excited spin states undergo non-radiative relaxation back to the equilibrium distribution of spin states. It is analogous to the excited-state lifetimes that appear in fluorescence and phosphorescence decays in electronic excited states.

The T2 relaxation process represents the decay of the net magnetization vector in the x-y plane. This process dominates the decay of the FID and is therefore involved in the detection of the signal.

T2 relaxation can be << than T1 so that following the decay of FID, the spin states have not returned to equilibrium

slide57

There are 2 relaxation process in spin resonance spectroscopy. These are referred to as: 1. transverse-, or spin-lattice relaxation time; T1 and, longitudinal- or spin-spin relaxation time; T2.

The T1 relaxation process denotes the process in which the excited spin states undergo non-radiative relaxation back to the equilibrium distribution of spin states. It is analogous to the excited-state lifetimes that appear in fluorescence and phosphorescence decays in electronic excited states.

The T2 relaxation process represents the decay of the net magnetization vector in the x-y plane. This process dominates the decay of the FID and is therefore involved in the detection of the signal.

T2 relaxation can be << than T1 so that following the decay of FID, the spin states have not returned to equilibrium

slide58

There are 2 relaxation process in spin resonance spectroscopy. These are referred to as: 1. transverse-, or spin-lattice relaxation time; T1 and, longitudinal- or spin-spin relaxation time; T2.

The T1 relaxation process denotes the process in which the excited spin states undergo non-radiative relaxation back to the equilibrium distribution of spin states. It is analogous to the excited-state lifetimes that appear in fluorescence and phosphorescence decays in electronic excited states.

The T2 relaxation process represents the decay of the net magnetization vector in the x-y plane. This process dominates the decay of the FID and is therefore involved in the detection of the signal.

T2 relaxation can be << than T1 so that at the end of the decay of FID, the spin states have not returned to equilibrium.

slide59

The measurement of T1 relaxation

  • Relaxation of non-equilibrium spin distribution back to equilibrium in the form of: i) inversion recovery i) decay from saturation.
  • The inversion recovery pulse sequence is denoted:
  • 180o – t – 90o
  • The sample is pulse-excited for: tpulse = i.e. twice as long as the 90o pulse (same B1 intensity). This excitation not only reduces the magnitude of the Mo in the z-direction (due to production of b spins) to the point as which Mo goes negative.
  • A 180o pulse causing the precession of Mo around y into the – z direction
slide60

The measurement of T1 relaxation

  • Relaxation of non-equilibrium spin distribution back to equilibrium in the form of: i) inversion recovery i) decay from saturation.
  • The inversion recovery pulse sequence is denoted:
  • 180o – t – 90o
  • The sample is pulse-excited for: tpulse = i.e. twice as long as the 90o pulse (same B1 intensity). This excitation not only reduces the magnitude of the Mo in the z-direction (due to production of b spins) to the point as which Mo goes negative.
  • A 180o pulse causing the precession of Mo around y into the – z direction
slide61

The measurement of T1 relaxation

  • Relaxation of non-equilibrium spin distribution back to equilibrium in the form of: i) inversion recovery i) decay from saturation.
  • The inversion recovery pulse sequence is denoted:
  • 180o – t – 90o
  • The sample is pulse-excited for: tpulse = i.e. twice as long as the 90o pulse (same B1 intensity). This excitation not only reduces the magnitude of the Mo in the z-direction (due to production of b spins) to the point as which Mo goes negative.
  • A 180o pulse causing the precession of Mo around y into the – z direction
slide62

The measurement of T1 relaxation

  • Relaxation of non-equilibrium spin distribution back to equilibrium in the form of: i) inversion recovery i) decay from saturation.
  • The inversion recovery pulse sequence is denoted:
  • 180o – t – 90o
  • The sample is pulse-excited for: tpulse = i.e. twice as long as the 90o pulse (same B1 intensity). This excitation not only reduces the magnitude of the Mo in the z-direction (due to production of b spins) to the point as which Mo goes negative.
  • A 180o pulse causing the precession of Mo around y into the – z direction
slide63

The signal, however, is detected from the oscillation of Mo in the x-y plane. In the 180o – t – 90o pulse sequences, the sample is excited with the B1 field with a pulse duration that rotates Mo into the -z direction. The population along –z is allowed to decay for a time t and then a 90o pulse is applied and the FID is measured The initial intensity is recorded and the sequence is repeated with increasingly longer t –values:

slide64

The initial negative intensity from the FID decays grow back to zero, becomes positive until it reaches the equilibrium value in the Bo field.

ii) Recovery from saturation. In this approach to the . measurement of T1, the sample is excited with a longer . pulse until the rates of absorption and stimulated emission . are equal.

. At this point Mo = 0 and the recovery to the positive . equilibrium value by again obtaining FID decays to obtain . the initial intensities at increasing delay times t.

slide65

The initial negative intensity from the FID decays grow back to zero, becomes positive until it reaches the equilibrium value in the Bo field.

slide66

The initial negative intensity from the FID decays grow back to zero, becomes positive until it reaches the equilibrium value in the Bo field.

ii) Recovery from saturation. In this approach to the . measurement of T1, the sample is excited with a longer . pulse until the rates of absorption and stimulated emission . are equal.

. At this point Mo = 0 and the recovery to the positive . equilibrium value by again obtaining FID decays to obtain . the initial intensities at increasing delay times t.

slide67

The initial negative intensity from the FID decays grow back to zero, becomes positive until it reaches the equilibrium value in the Bo field.

ii) Recovery from saturation. In this approach to the . measurement of T1, the sample is excited with a longer . pulse until the rates of absorption and stimulated emission . are equal.

. At this point Mo = 0 and the recovery to the positive . equilibrium value by again obtaining FID decays to obtain . the initial intensities at increasing delay times t.