apimba - User contributions [en]

Walk-up NMR user instructions for Nanalysis

2020-05-16T22:18:57Z

72.12.192.208:

This machine is so easy to use that one video by the manufacturer covers everything:
[https://www.youtube.com/watch?v=lcc0VkE9Ya0 Demonstration of basic Nanalysis proton NMR spectrum collection]

Macro view of NMR

2020-04-23T08:41:40Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.
Image of precessing dipole

Then a transmitter in an axis orthogonal to the main magnetic field (B0) sends an Rf pulse, which creates a new magnetic field called B1:

[[File:Helmholtz_with_tube.jpg|200px]]

Since the dipole magnet is precessing, it is common to look at the Z-component of the dipole magnet vector, called Mz.The new magnetic field B1 pulls the net dipole down into the XY plane, and since the Rf is oscillating the new magnetic field B1 cycles plus and minus and will cause the dipole to push all the way to -Z and back up to +Z again, depending on how long the Rf pulse is.

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Macro view of NMR

2020-04-23T08:13:46Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.
Image of precessing dipole

Then a transmitter in an axis orthogonal to the main magnetic field (B0) sends an Rf pulse, which creates a new magnetic field called B1:

[[File:Helmholtz_with_tube.jpg|200px]]

The new magnetic field B1 pulls the net dipole down into the XY plane, and since the Rf is oscillating the new magnetic field B1 cycles plus and minus and will cause the dipole to push all the way to -Z and back up to +Z again, depending on how long the Rf pulse is.

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Macro view of NMR

2020-04-23T07:58:39Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.
Image of precessing dipole

Then a transmitter in an axis orthogonal to the main magnetic field (B0) sends an Rf pulse, which creates a new magnetic field called B1:

[[File:Helmholtz_with_tube.jpg|200px]]

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Macro view of NMR

2020-04-23T07:57:44Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.
Image of precessing dipole

Then a transmitter in an axis orthogonal to the main magnetic field sends an Rf pulse:

[[File:Helmholtz_with_tube.jpg|200px]]

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Macro view of NMR

2020-04-23T07:56:15Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.

[[File:Helmholtz_with_tube.jpg|200px]]

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Macro view of NMR

2020-04-23T07:56:04Z

72.12.192.208: /* Radio Pulse Power vs Transition Pulse Power */

==Magnetism instead of [[Micro view of NMR#Quantum transitions in nuclei|transitions]]==
NMR at the level of the sample rather than the nucleus requires a complete change of thinking and a lot of math. The focus on the main page will be the thinking part, the math can be accessed on separate pages via links. The instrument utilizes magnetic induction rather than photon absorption. A transmitter causes changes in the magnetic fields of a sample, which then induce currents in a detector coil which are picked up by a receiver. So understanding NMR at a macro level requires intimate knowledge of [[Magnetic Moment|magnetic moments]] and [[Induction|induction]].

First the sample has to be defined. Ethanol is a good starting sample for analysis. It is a simple molecule, a liquid at room temperature with good flow rate (low viscosity) and slow evaporation rate (low vapor pressure). The molecule has 6 hydrogens, 2 carbons and an oxygen (CH3CH2OH), and there is not much self-association at room temperature. The sample container will be a 5mm glass tube:

[[file:NMR_tube.jpg|100px]]

About 0.75ml of ethanol in the tube will make a perfect sample for introduction to NMR.

All matter that is charged also has a magnetic field. Why? Good luck with that. Technically, if a charge isn't moving it isn't supposed to have a magnetic field, but since movement is relative, everything is moving compared to something else, so everything that is charged has a magnetic field. At any rate, since every atom has positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus, there should be a net magnetic field around each atom. Similarly, there should be a net magnetic field around every molecule since the atoms are bonded to each other via electrons which all have charge and thus magnetic fields. However, a complication to this picture is that atoms and electrons also have a property called spin, and this property affects an atom's net magnetic field, and thus whether there is an actual net magnetic field.

It turns out that the main 1H isotope of hydrogen (called proton in the NMR literature) and the [[Table of NMR Isotopes|13C]] isotope of carbon (called carbon in the NMR literature) have net magnetic fields while the main isotope of oxygen and the main 12C isomer of carbon do not.

In summary, in the NMR tube of ethanol there is a solution of tiny bar magnets of 1H and 13C.

On the benchtop, the bar magnets floating around in solution are randomly oriented, so the bar magnets average out. If placed into a strong magnetic field however, some of the floating bar magnets will line up with the field, generating a net magnetic field for each 1H and 13C. If magnetism was the only factor then the floating bar magnets would line up with the external field and that would be it, nothing more would happen. The key part about NMR is that these magnets are also spinning, so there is torque that causes a [[Precession|precession]] around the axis of the external field. '''This precession frequency is what is probed with a transmitter'''.

==Spectra vs [[Micro view of NMR#Spectra|Transition Spectra]]==
To obtain a spectrum, the sample is placed into a static magnetic field to cause alignment of the magnets within a sample and their precession about the external magnetic field axis. This frequency depends on the [[gyromagnetic ratio]] (gamma) (g) for that element/elementary particle (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

Since this v0 is a moving charge, this represents electromagnetic frequency and can interact with an external electromagnetic frequency according to the usual rules of [[Wave Mechanics in NMR|wave mechanics]]. In short, if an external electromagnetic frequency of the same magnitude is applied to the sample, it can 'resonate' with the sample, depending on the phases of the two fields. Fortunately, the gyromagnetic ratios of components of a sample are dramatically different, so a transmitter/receiver pair can be set up to 'look' at just one of the many v0 in a sample.

Based on the Larmor equation, the only variable for a particular atomic component is the external field strength B0, but since there are magnetic fields all around a molecule of the sample, each atomic component will experience slightly different B, and thus have slightly different v. Thus the transmitter/receiver pair will see several resonances for each atomic component in a sample of a molecule such as ethanol and it is these resonances that are studied in NMR. In addition, the atoms in a molecule that are in the same magnetic environment will experience the same B and thus have the same v and give the same peak.

For the sample of ethanol there are three groups of protons, and two groups of carbons, so there should be 3 peaks in the proton spectrum and 2 peaks in the carbon spectrum (the splitting in the proton spectrum and lack of splitting in the carbon spectrum will be discussed [[#Peak Splitting vs Transition Peak Splitting|later]]):

[[File:proton NMR of ethanol.png|500px]]

[[File:13C NMR ethanol.png|200px]]

For both spectra the x axis is relative frequency while the y axis is relative intensity.

==Radio Pulse Power vs [[Micro view of NMR#Radio pulse power|Transition Pulse Power]]==
Radio pulse power is where the macro view of NMR changes dramatically from micro view. The situation at the start of an experiment is the sample suspended in a strong magnetic field so any net magnetic dipoles start precessing around the external magnetic field axis.

[[File:Helmholtz_with_tube.jpg|50px]]

==Saturation vs. [[Micro view of NMR#Saturation|Transition Saturation]]==

==Peak Intensity vs [[Micro view of NMR#Peak Intensity|Transition Intensity]]==

==Sensitivity vs [[Micro view of NMR#Sensitivity|Transition Sensitivity]]==

==Peak Splitting vs [[Micro view of NMR#Peak Splitting|Transition Peak Splitting]]==

==Relaxation vs [[Micro view of NMR#Relaxation|Transition Relaxation]]==

==Related Topics==

Main Page

2020-04-22T08:52:53Z

72.12.192.208: /* List of sections in this wiki */

==[[Aeri Park|Apimba]]==
I was online before there was an internet. When it first came out the internet had great promise for science since it was a place that people could go to for sharing knowledge. Science advanced faster since learning the current status of a field of research could be done quicker and easier. I had many links to great resources that enhanced my research and allowed me to progress in my field. The internet is forever was the idea.

However, greed got the better of things and that promise withered. Domain names started requiring annual fees, which meant that domain owners had to continuously pay to keep their site online. The internet is forever was no longer true. Then scientific journals started locking up their content behind paywalls, even though the work was done by government agencies funded by the general public. Knowledge sharing also ended and the advance of knowledge slowed down. Universities started restricting access to their research. It now takes much longer to learn enough about a particular field to be able to add to it. The final straw for me was when university and research center libraries started to restrict access, which not only makes it harder to learn what is needed to get up to speed in a field, it also permits the spread of ignorance in the general public since they cannot get to the fundamental research on a topic.

Monetization became the driving force and, one by one, the resources disappeared and the links stopped working. This wiki is an attempt to salvage what is left of those resources and save them for future generations. As a result, most of the content in this wiki is from other sources, including Wikipedia, since I foresee the day when even that resource goes away or is restricted behind a paywall. The main difference in this wiki is that it focuses on knowledge, not citations or history or language. This wiki is a place to learn, not find out who did what and when.

I will also focus on areas that I know well, using it as a bank to store my knowledge and the collected knowledge of the fields that I worked in.

Link to [http://www.apimba.org/ Apimba home page].

==List of sections in this wiki==
#[[NMR|Nuclear Magnetic Resonance (NMR)]]
#[[Getting started|Making changes to the wiki]]

NMR Pulse Sequences

2020-04-22T08:05:10Z

72.12.192.208: /* Listing */

List of pulse sequences, details, examples.
==General Information==

==Terminology==

==Listing==
* [[Standard 1 pulse NMR sequence|default]] - probably 95% of all experiments use this.
* [[Standard 1 pulse NMR sequence with Presaturation|Presaturation]] - minimizes large peaks such as residual solvent.
* [[Standard proton decoupled pulse NMR sequence|proton decoupled]] - increases sensitivity of nuclei other than proton.
* [[2D COSY pulse NMR sequence|COSY]] - correlated proton
* [[NOESY pulse NMR sequence|NOESY]] - through space interaction proton
* [[2D HSQC pulse NMR sequence|HSQC]] - proton carbon correlation

==Other Information==
* [[Bruker Pulse Sequence Catalog]]
* [https://www.bruker.com/fileadmin/user_upload/8-PDF-Docs/MagneticResonance/Service_NMR/Prgramming-Manuals/pulse_programming.pdf Creating New Pulse Sequences for Bruker Instruments]
* [https://spin.niddk.nih.gov/bax/pp/ Ad Bax group pulse sequences]

NMR Pulse Sequences

2020-04-22T08:03:07Z

72.12.192.208: /* Listing */

List of pulse sequences, details, examples.
==General Information==

==Terminology==

==Listing==
* [[Standard 1 pulse NMR sequence|default]] - probably 95% of all experiments use this.
* [[Standard 1 pulse NMR sequence with Presaturation|Presaturation]]
* [[Standard proton decoupled pulse NMR sequence|proton decoupled]]
* [[2D COSY pulse NMR sequence|COSY]]
* [[NOESY pulse NMR sequence|NOESY]]
* [[2D HSQC pulse NMR sequence|HSQC]]

==Other Information==
* [[Bruker Pulse Sequence Catalog]]
* [https://www.bruker.com/fileadmin/user_upload/8-PDF-Docs/MagneticResonance/Service_NMR/Prgramming-Manuals/pulse_programming.pdf Creating New Pulse Sequences for Bruker Instruments]
* [https://spin.niddk.nih.gov/bax/pp/ Ad Bax group pulse sequences]

Micro view of NMR

2020-04-17T00:38:32Z

72.12.192.208: /* Peak Splitting */

==Quantum transitions in nuclei==
NMR from a micro-point of view is an instrumental technique that uses photons of radio frequency energy to [[Resonance in NMR|cause]] a transition, or change in state, in an atom. Radio is used because the amount of energy needed to cause these transitions happens to fall in the radio region of the [[electromagnetic spectrum]]. The transitions are also quantized, which means there has to be the right amount of energy to cause a change of state, too much or too little and no change occurs.

There are many quantum transitions in atoms, but the ones manipulated in NMR are [[Quantum spin|quantum spin]] transitions. Quantum spin has two states, often referred to as "up" and "down". In a natural environment these two states are equivalent in energy, so an atom could be in one or the other at any time with no change in energy. However, when the atom is placed in a strong magnetic field the states become non-equivalent, with one of the states a little higher in energy than the other. '''This difference in energy is the key to NMR.''' A photon with this amount of energy can then be shot at the atom, which will absorb it and cause a transition between the 'up' and 'down' spin states. Thus light can be used to probe substances at the atom level!

Note that the atom hasn't changed. It is still the same atom when it is placed in a magnetic field. Only the potential spin state energies have changed. Everything about atoms is discussed in probabilities, so the way to say it is that the spin state of the atom in a magnetic field is ''most likely'' the lower energy state.

At the atomic size scale, atoms are composed of protons and neutrons and electrons. All three of these have the same quantum spin and can be studied when placed in a strong magnetic field and pulsed with photons. Transitions are at different energies for the three types of subatomic particle so instruments are designed to look at them independently: Electron Spin Resonance (ESR or EPR) for electron spins and Nuclear Magnetic Resonance (NMR) for nuclear spins. For NMR, the hydrogen atom has just a single proton in its nucleus so the physics of spin transitions are easiest to study for this element. Other elements have many protons and neutrons so the [[net nuclear spin]], called I, is considered when studying their spin transitions.

Net nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found across the entire periodic table. Protons and neutrons each have net spin of ½, but this derives from the elementary quarks and gluons of which they are composed. As a result of this complexity, no simple formula exists to predict I based on the [[Spins of nuclei|number of protons and neutrons within an atom]].

The formula for the number of states = 2I+1, thus a spin 1/2 nucleus such as a single hydrogen atom will have 2 states and 1 transition (when placed in a static magnetic field). For I greater than 1/2 there are more than two states and thus many transitions. Spin 1/2 nuclei are the best for NMR since two states with one transition gives good, clean spectra that are easily interpretable. A lot of information about the environment of a nucleus can thus be obtained, making 1H NMR the most useful analytical technique in science.

From here on, the focus will be on spin 1/2 nuclei, specifically 1H. This nucleus is referred to as "proton" in the NMR literature, but other [[Spins of nuclei|spin 1/2 nuclei]] behave the same. Nuclei with spins other than 1/2 will have more than one transition and give much more complicated spectra, so these will be explored in another section.

==Spectra==
To obtain a spectrum, a spin 1/2 atom must first be placed into a static magnetic field to cause separation of the two states. The amount of separation depends on the [[gyromagnetic ratio]] (gamma) (g) for that element (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

The atom is then pulsed with a composite radio wave that includes the [[Relationship between frequency and energy|frequency]] v0, called the Larmor Frequency. The atom absorbs just the v0 part of the radio wave (since it is a quantum transition), and a detector in the same axis as the radio wave (usually the same antenna) is then turned on to receive any emitted energy.

Making this happen in an instrument is thus mainly an [[NMR from an Instrument point of view|engineering problem]].

From the equation above, since g is a constant for each element and B0 is a constant (it is a measure of the magnetic field strength in that instrument in the units of Tesla), there is just one frequency for that proton, which makes sense since there is just one transition, thus there is just one peak expected in the spectrum. In reality though, an atom never exists in isolation, so it never experiences the pure B0. The actual frequency ''v'' is thus slightly different for atoms of a particular g based on the actual magnetic field around the atom. These slight differences in frequency are what gives a spectrum of peaks for a molecule rather than a single peak. There is still just one transition for that atom type (if that type is spin 1/2, such as 1H), but the transition energy is different for each 1H that is in a different magnetic environment.

If the 1H is part of a molecule then 1H atoms in the molecule in similar magnetic environments can be grouped and can be expected to give one peak per group.

To see examples, the view will be increased beyond a single 1H atom and into a collection of 1H atoms as part of molecules, such as a solution of one compound in a solvent or a pure liquid, such as ethanol.

For a sample of ethanol (CH3CH2OH), we first have to list the spin 1/2 groups in the sample:
1H and 13C

*Fortunately, the g for 1H and 13C are [[Gyromagnetic ratio|very different]], which means that the radio frequencies needed to cause spin transitions are [[Nuclear Range in NMR|also different]]. If a narrow band of radio is used both to transmit and receive, it is possible to "see" 1H and 13C separately. In other words, when looking at 1H, the 13C will not be excited because the quantum energy is not correct. The 13C are invisible in 1H spectra, and the 1H are invisible in 13C spectra.

Next is a listing of 1H groups in the sample:

A group for the protons in the CH3 of ethanol

A group for the protons in the CH2 of ethanol

A group for the OH of ethanol.

Thus three peaks are expected in the 1H spectrum of this sample (the splitting of the peaks will be discussed [[#Peak Splitting|later]]).

[[File:proton NMR of ethanol.png|500px]]

The units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity.

*Another spin 1/2 nucleus in this sample is carbon, specifically the 13C isotope. Based on the [[Table of NMR Isotopes|isotope abundance table]], 13C is only 1.11% of the total carbon atoms in a sample. The other carbon atoms have spin 0 and are not visible in NMR, so, if the instrument is sensitive enough, it can detect the 1.1% of carbons in a sample that are spin 1/2.

A list of possible 13C carbons in the sample:

A group for the CH3 of ethanol

A group for the CH2 of ethanol.

There are no other carbon sources in this sample so there should be just 2 peaks in the spectrum (the lack of splitting will be discussed later).

[[File:13C NMR ethanol.png|200px]]

Again, the units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity. The ppm range is different than for the proton NMR spectrum because the g is different for the two nuclei, which makes the v0 different.

==Radio pulse power==
How powerful should the radio pulse be to get a good signal? Each transition requires one photon, so enough photons are needed in a pulse to cause transitions in all the nuclei in a sample. The total number of photons in a pulse of radio is the power of the pulse times the length of time that the pulse is turned on, where power is given in watts (W) and time in microseconds (µ). It is then a simple matter of running multiple experiments using different power and time settings until the maximum signal is achieved. The ideal numbers are actually limited by technical problems such as transmitter parameters and timing capabilities.

The pulse length at a specific power that gives the maximum signal is called the 90 degree pulse (for historic reasons).

==Saturation==
Since NMR looks at quantum transitions of nuclei, only at absolute zero will all the nuclei be in the lowest energy state. At other temperatures there is a population in both states, with a slight excess in the lower energy state at room temperature. The equation describing this is called the [[Boltzmann Distribution| Boltzmann distribution]], which holds at thermal equilibrium:

(number of nuclei in the higher state)/(number of nuclei in the lower state) = e-(difference in energies/a constant*absolute temperature)

Nh/Nl = e-DE/kT

An NMR signal is only obtained when there is emission of a photon, so only the slight excess in the lower state is 'available' for excitation and subsequent emission of a photon. Thus as more and more photons are included in the pulse, at some point the populations will equalize and there will be no more transitions and no more signal. Then, as more photons are added the populations will invert since the system is no longer at equilibrium, making the higher energy state slightly more populated. This will 'invert' the phase of the photons that are emitted after excitation. All these pulse lengths have names:

* 90 degree pulse - first maximum signal
* 180 degree pulse - first minimum signal
* 270 degree pulse - second maximum signal but inverted phase
* 360 degree pulse - second minimum signal

==Peak Intensity==
The next topic is an explanation for how big the peaks in the spectrum are. Since there is one photon absorbed per nuclear transition, if photons could be counted then it would give the number of excitable nuclei in the sample (subject to boltzmann distribution described in the saturation section). Photon counts are represented by areas of peaks in spectra. This makes NMR a potentially quantitative method. The complication is that it is assumed that all excited nuclei release their photons at the same time so that the detector can see them. For 1H NMR this is mostly true, but for other nuclei it is not true since other factors such as delay in photon emission depending on the environment causing it to no longer be quantitative.

==Sensitivity==
Since this technique involves photon absorption by individual nuclei, the more nuclei in the sample the stronger the signal. For 1H, all protons in a natural abundance sample are 1H and thus all are available for excitation.13C is only 1.1% of a natural abundance sample so this nucleus will be much less sensitive. The transition energy also influences the population difference in the Boltzmann equation which further alters the sensitivity of a particular nucleus. Sample size and other factors affect overall sensitivity. There are a number of equations that have been developed to attempt to quantify how these factors influence the sensitivity in an experiment.

==Peak Splitting==
In the 1H spectrum of ethanol [[#Spectra|above]], two of the peaks are split into multiplets: a triplet and a quartet. The quartet is from the CH2, while the triplet is from the CH3. Remember that each group of magnetically equivalent 1H has one potential transition, so the apparent splitting of the peaks must be due to the environment around the nucleus, rather than the nucleus itself. Remember also that the location of the transition peak is due to the strength of the local magnetic field, which is different from the external magnetic field B0 because of electrons and other nuclei in the molecule. Combining these two concepts suggests that splitting of a nucleus is due to the presence of multiple populations of neighboring nuclei and electrons.

Fortunately, electrons in bonds are paired and have net spin 0, so they don't have multiple states when placed in a magnetic field. Carbons also have net spin 0 so they don't have multiple states either (13C does have two states but is present at only 1.1% of total carbon). Therefore the only source of multiple states in ethanol is other hydrogens. In a sample, the total 1H population is split into two for each 1H on the molecule due to the Boltzmann distribution as described previously. So the methyl protons in ethanol see four different environments due to the two populations of each 1H on the neighboring CH2. Four different magnetic environments thus leads to 4 different peaks for the methyl. Symmetry of the CH2 means that two of the four overlap, resulting in three peaks, with the central peak double in size.

[[File:splitting.gif|600px]]

Following the same logic, the CH2 in ethanol will have 6 peaks due to 6 different environments, two environments for each 1H in the methyl, with 4 of them overlapping due to symmetry of the methyl protons, resulting in a quartet.

In summary, 'splitting' of a peak in NMR is actually multiple peaks, with each peak in the multiplet representing one transition per environment. Overlap of the peaks due to symmetry is what gives an apparent multiplet. The distance between the peaks in a multiplet is called the coupling constant, J, and is displayed in Hertz.

==Relaxation==
A sample of menthyl anthranilate is placed into a strong magnetic field and pulsed with radio frequency photons in the 1H range. The excess population of protons that are in the lower energy state are excited into the higher energy state. The transmitter is turned off and the receiver is turned on. Then what?

Thermodynamics as embodied in the Boltzmann Distribution will drive the states back to equilibrium again, but it will not happen all at once. The process of states returning to equilibration is called relaxation. The image below is what the signal looks like once the receiver is turned on. There is an initial burst of photons, then a gradual decrease over time as the remaining protons return to the lower state:

[[File:fid menthyl anthranilate.png|300px]]

bottom axis is time in seconds

A good way to think of it is hitting a bell with a hammer. Even though the initial impulse of the hammer is over, the bell continues to ring at the same frequencies but with decreasing intensity over time.

The delay in states relaxing back to equilibration occurs due to several mechanisms:
* Dipole-dipole interaction
* Chemical shift anisotropy
* Quadrupolar interaction (if I>=1)
* Spin-rotation
* Scalar
* Paramagnetic

[[Relaxation of spin 1/2 nuclei: two-state derivation|Relaxation Math - 2 states]]

[[Relaxation of spin 1/2 nuclei: transition probabilities|Relaxation Math - transition probabilities]]

The equations for relaxation are complex and generally involve two numbers: the spin-lattice relaxation time T1 and the spin-spin relaxation time T2. Because both mechanisms are happening at the same time it is difficult to measure them independently, so a number of unique experiments have been designed to try to minimize the overlap in the times.

==Related topics==
* [[Quantum spin|Quantum spin]]
* [[Gyromagnetic ratio]]
* [[Spins of nuclei]]
* [[Net nuclear spin]]
* [[Table of NMR Isotopes|Isotope abundance]]
* [[Boltzmann Distribution|Boltzmann Distribution]]

Micro view of NMR

2020-04-17T00:38:20Z

72.12.192.208: /* Peak Splitting */

==Quantum transitions in nuclei==
NMR from a micro-point of view is an instrumental technique that uses photons of radio frequency energy to [[Resonance in NMR|cause]] a transition, or change in state, in an atom. Radio is used because the amount of energy needed to cause these transitions happens to fall in the radio region of the [[electromagnetic spectrum]]. The transitions are also quantized, which means there has to be the right amount of energy to cause a change of state, too much or too little and no change occurs.

There are many quantum transitions in atoms, but the ones manipulated in NMR are [[Quantum spin|quantum spin]] transitions. Quantum spin has two states, often referred to as "up" and "down". In a natural environment these two states are equivalent in energy, so an atom could be in one or the other at any time with no change in energy. However, when the atom is placed in a strong magnetic field the states become non-equivalent, with one of the states a little higher in energy than the other. '''This difference in energy is the key to NMR.''' A photon with this amount of energy can then be shot at the atom, which will absorb it and cause a transition between the 'up' and 'down' spin states. Thus light can be used to probe substances at the atom level!

Note that the atom hasn't changed. It is still the same atom when it is placed in a magnetic field. Only the potential spin state energies have changed. Everything about atoms is discussed in probabilities, so the way to say it is that the spin state of the atom in a magnetic field is ''most likely'' the lower energy state.

At the atomic size scale, atoms are composed of protons and neutrons and electrons. All three of these have the same quantum spin and can be studied when placed in a strong magnetic field and pulsed with photons. Transitions are at different energies for the three types of subatomic particle so instruments are designed to look at them independently: Electron Spin Resonance (ESR or EPR) for electron spins and Nuclear Magnetic Resonance (NMR) for nuclear spins. For NMR, the hydrogen atom has just a single proton in its nucleus so the physics of spin transitions are easiest to study for this element. Other elements have many protons and neutrons so the [[net nuclear spin]], called I, is considered when studying their spin transitions.

Net nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found across the entire periodic table. Protons and neutrons each have net spin of ½, but this derives from the elementary quarks and gluons of which they are composed. As a result of this complexity, no simple formula exists to predict I based on the [[Spins of nuclei|number of protons and neutrons within an atom]].

The formula for the number of states = 2I+1, thus a spin 1/2 nucleus such as a single hydrogen atom will have 2 states and 1 transition (when placed in a static magnetic field). For I greater than 1/2 there are more than two states and thus many transitions. Spin 1/2 nuclei are the best for NMR since two states with one transition gives good, clean spectra that are easily interpretable. A lot of information about the environment of a nucleus can thus be obtained, making 1H NMR the most useful analytical technique in science.

From here on, the focus will be on spin 1/2 nuclei, specifically 1H. This nucleus is referred to as "proton" in the NMR literature, but other [[Spins of nuclei|spin 1/2 nuclei]] behave the same. Nuclei with spins other than 1/2 will have more than one transition and give much more complicated spectra, so these will be explored in another section.

==Spectra==
To obtain a spectrum, a spin 1/2 atom must first be placed into a static magnetic field to cause separation of the two states. The amount of separation depends on the [[gyromagnetic ratio]] (gamma) (g) for that element (a constant) and the intensity of the static magnetic field (B0) according to the [[Derivation of Larmor frequency equation|derived equation]]:

v0=g*B0

The atom is then pulsed with a composite radio wave that includes the [[Relationship between frequency and energy|frequency]] v0, called the Larmor Frequency. The atom absorbs just the v0 part of the radio wave (since it is a quantum transition), and a detector in the same axis as the radio wave (usually the same antenna) is then turned on to receive any emitted energy.

Making this happen in an instrument is thus mainly an [[NMR from an Instrument point of view|engineering problem]].

From the equation above, since g is a constant for each element and B0 is a constant (it is a measure of the magnetic field strength in that instrument in the units of Tesla), there is just one frequency for that proton, which makes sense since there is just one transition, thus there is just one peak expected in the spectrum. In reality though, an atom never exists in isolation, so it never experiences the pure B0. The actual frequency ''v'' is thus slightly different for atoms of a particular g based on the actual magnetic field around the atom. These slight differences in frequency are what gives a spectrum of peaks for a molecule rather than a single peak. There is still just one transition for that atom type (if that type is spin 1/2, such as 1H), but the transition energy is different for each 1H that is in a different magnetic environment.

If the 1H is part of a molecule then 1H atoms in the molecule in similar magnetic environments can be grouped and can be expected to give one peak per group.

To see examples, the view will be increased beyond a single 1H atom and into a collection of 1H atoms as part of molecules, such as a solution of one compound in a solvent or a pure liquid, such as ethanol.

For a sample of ethanol (CH3CH2OH), we first have to list the spin 1/2 groups in the sample:
1H and 13C

*Fortunately, the g for 1H and 13C are [[Gyromagnetic ratio|very different]], which means that the radio frequencies needed to cause spin transitions are [[Nuclear Range in NMR|also different]]. If a narrow band of radio is used both to transmit and receive, it is possible to "see" 1H and 13C separately. In other words, when looking at 1H, the 13C will not be excited because the quantum energy is not correct. The 13C are invisible in 1H spectra, and the 1H are invisible in 13C spectra.

Next is a listing of 1H groups in the sample:

A group for the protons in the CH3 of ethanol

A group for the protons in the CH2 of ethanol

A group for the OH of ethanol.

Thus three peaks are expected in the 1H spectrum of this sample (the splitting of the peaks will be discussed [[#Peak Splitting|later]]).

[[File:proton NMR of ethanol.png|500px]]

The units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity.

*Another spin 1/2 nucleus in this sample is carbon, specifically the 13C isotope. Based on the [[Table of NMR Isotopes|isotope abundance table]], 13C is only 1.11% of the total carbon atoms in a sample. The other carbon atoms have spin 0 and are not visible in NMR, so, if the instrument is sensitive enough, it can detect the 1.1% of carbons in a sample that are spin 1/2.

A list of possible 13C carbons in the sample:

A group for the CH3 of ethanol

A group for the CH2 of ethanol.

There are no other carbon sources in this sample so there should be just 2 peaks in the spectrum (the lack of splitting will be discussed later).

[[File:13C NMR ethanol.png|200px]]

Again, the units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity. The ppm range is different than for the proton NMR spectrum because the g is different for the two nuclei, which makes the v0 different.

==Radio pulse power==
How powerful should the radio pulse be to get a good signal? Each transition requires one photon, so enough photons are needed in a pulse to cause transitions in all the nuclei in a sample. The total number of photons in a pulse of radio is the power of the pulse times the length of time that the pulse is turned on, where power is given in watts (W) and time in microseconds (µ). It is then a simple matter of running multiple experiments using different power and time settings until the maximum signal is achieved. The ideal numbers are actually limited by technical problems such as transmitter parameters and timing capabilities.

The pulse length at a specific power that gives the maximum signal is called the 90 degree pulse (for historic reasons).

==Saturation==
Since NMR looks at quantum transitions of nuclei, only at absolute zero will all the nuclei be in the lowest energy state. At other temperatures there is a population in both states, with a slight excess in the lower energy state at room temperature. The equation describing this is called the [[Boltzmann Distribution| Boltzmann distribution]], which holds at thermal equilibrium:

(number of nuclei in the higher state)/(number of nuclei in the lower state) = e-(difference in energies/a constant*absolute temperature)

Nh/Nl = e-DE/kT

An NMR signal is only obtained when there is emission of a photon, so only the slight excess in the lower state is 'available' for excitation and subsequent emission of a photon. Thus as more and more photons are included in the pulse, at some point the populations will equalize and there will be no more transitions and no more signal. Then, as more photons are added the populations will invert since the system is no longer at equilibrium, making the higher energy state slightly more populated. This will 'invert' the phase of the photons that are emitted after excitation. All these pulse lengths have names:

* 90 degree pulse - first maximum signal
* 180 degree pulse - first minimum signal
* 270 degree pulse - second maximum signal but inverted phase
* 360 degree pulse - second minimum signal

==Peak Intensity==
The next topic is an explanation for how big the peaks in the spectrum are. Since there is one photon absorbed per nuclear transition, if photons could be counted then it would give the number of excitable nuclei in the sample (subject to boltzmann distribution described in the saturation section). Photon counts are represented by areas of peaks in spectra. This makes NMR a potentially quantitative method. The complication is that it is assumed that all excited nuclei release their photons at the same time so that the detector can see them. For 1H NMR this is mostly true, but for other nuclei it is not true since other factors such as delay in photon emission depending on the environment causing it to no longer be quantitative.

==Sensitivity==
Since this technique involves photon absorption by individual nuclei, the more nuclei in the sample the stronger the signal. For 1H, all protons in a natural abundance sample are 1H and thus all are available for excitation.13C is only 1.1% of a natural abundance sample so this nucleus will be much less sensitive. The transition energy also influences the population difference in the Boltzmann equation which further alters the sensitivity of a particular nucleus. Sample size and other factors affect overall sensitivity. There are a number of equations that have been developed to attempt to quantify how these factors influence the sensitivity in an experiment.

==Peak Splitting==
In the 1H spectrum of ethanol [[#Spectra|above]], two of the peaks are split into multiplets: a triplet and a quartet. The quartet is from the CH2, while the triplet is from the CH3. Remember that each group of magnetically equivalent 1H has one potential transition, so the apparent splitting of the peaks must be due to the environment around the nucleus, rather than the nucleus itself. Remember also that the location of the transition peak is due to the strength of the local magnetic field, which is different from the external magnetic field B0 because of electrons and other nuclei in the molecule. Combining these two concepts suggests that splitting of a nucleus is due to the presence of multiple populations of neighboring nuclei and electrons.

Fortunately, electrons in bonds are paired and have net spin 0, so they don't have multiple states when placed in a magnetic field. Carbons also have net spin 0 so they don't have multiple states either (13C does have two states but is present at only 1.1% of total carbon). Therefore the only source of multiple states in ethanol is other hydrogens. In a sample, the total 1H population is split into two for each 1H on the molecule due to the Boltzmann distribution as described previously. So the methyl protons in ethanol see four different environments due to the two populations of each 1H on the neighboring CH2. Four different magnetic environments thus leads to 4 different peaks for the methyl. Symmetry of the CH2 means that two of the four overlap, resulting in three peaks, with the central peak double in size.

[[File:splitting.gif|300px]]

Following the same logic, the CH2 in ethanol will have 6 peaks due to 6 different environments, two environments for each 1H in the methyl, with 4 of them overlapping due to symmetry of the methyl protons, resulting in a quartet.

In summary, 'splitting' of a peak in NMR is actually multiple peaks, with each peak in the multiplet representing one transition per environment. Overlap of the peaks due to symmetry is what gives an apparent multiplet. The distance between the peaks in a multiplet is called the coupling constant, J, and is displayed in Hertz.

==Relaxation==
A sample of menthyl anthranilate is placed into a strong magnetic field and pulsed with radio frequency photons in the 1H range. The excess population of protons that are in the lower energy state are excited into the higher energy state. The transmitter is turned off and the receiver is turned on. Then what?

Thermodynamics as embodied in the Boltzmann Distribution will drive the states back to equilibrium again, but it will not happen all at once. The process of states returning to equilibration is called relaxation. The image below is what the signal looks like once the receiver is turned on. There is an initial burst of photons, then a gradual decrease over time as the remaining protons return to the lower state:

[[File:fid menthyl anthranilate.png|300px]]

bottom axis is time in seconds

A good way to think of it is hitting a bell with a hammer. Even though the initial impulse of the hammer is over, the bell continues to ring at the same frequencies but with decreasing intensity over time.

The delay in states relaxing back to equilibration occurs due to several mechanisms:
* Dipole-dipole interaction
* Chemical shift anisotropy
* Quadrupolar interaction (if I>=1)
* Spin-rotation
* Scalar
* Paramagnetic

[[Relaxation of spin 1/2 nuclei: two-state derivation|Relaxation Math - 2 states]]

[[Relaxation of spin 1/2 nuclei: transition probabilities|Relaxation Math - transition probabilities]]

The equations for relaxation are complex and generally involve two numbers: the spin-lattice relaxation time T1 and the spin-spin relaxation time T2. Because both mechanisms are happening at the same time it is difficult to measure them independently, so a number of unique experiments have been designed to try to minimize the overlap in the times.

==Related topics==
* [[Quantum spin|Quantum spin]]
* [[Gyromagnetic ratio]]
* [[Spins of nuclei]]
* [[Net nuclear spin]]
* [[Table of NMR Isotopes|Isotope abundance]]
* [[Boltzmann Distribution|Boltzmann Distribution]]

Micro view of NMR

2020-03-19T17:08:22Z

72.12.192.208: /* Peak Intensity */

==Quantum transitions in nuclei==
In the micro view of NMR, it is an instrumental technique that uses photons of radio frequency energy to cause a transition, or change in state, in an atom. Radio is used because transitions at the atomic level are quantized, and the amount of energy needed to cause these transitions happens to fall in the radio region of the [[electromagnetic spectrum]]. Quantized energy means there has to be the right amount of energy to cause a change of state, too much or too little and no change occurs.

There are many quantum transitions in atoms, but the ones of interest in NMR are [[Quantum spin|quantum spin]] transitions of protons and neutrons. Quantum spin in protons and neutrons has two states, which are normally equivalent, but when placed in a magnetic field they become non-equivalent, so adding the appropriate sized photon of energy can cause a transition from one to the other. This works fine for single protons and neutrons, but when these are combined into a nucleus the situation gets more complex and we have to rely on a [[net nuclear spin]], called I.

Across the entire periodic table, net nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found. Protons and neutrons each have net spin of ½, but this derives from the elementary quarks and gluons of which they are composed. As a result of this complexity, no simple formula exists to predict I based on the [[Spins of nuclei|number of protons and neutrons within an atom]].

The formula for the number of states = 2I+1, thus a spin 1/2 nucleus such as a single hydrogen atom will have 2 states and 1 transition (when placed in a static magnetic field). For I greater than 1/2 there are more than two states and thus many transitions. The focus in NMR is on spin 1/2 nuclei since two states with one transition gives good, clean spectra that are easily interpretable. A lot of information about the environment of a nucleus can thus be obtained, making 1H NMR the most useful analytical technique in science.

From here on, the focus will be on spin 1/2 nuclei, specifically 1H. This nucleus is referred to as "proton" in the NMR literature, but other [[Spins of nuclei|spin 1/2 nuclei]] behave the same. Nuclei with spins other than 1/2 will have more than one transition and give much more complicated spectra, so these will be explored in another section.

==Spectra==
To obtain a spectrum, a spin 1/2 atom must first be placed into a static magnetic field to cause separation of the two states. The amount of separation depends on the [[gyromagnetic ratio]] (gamma) (g) for that element (a constant) and the intensity of the static magnetic field (B0) according to the equation:

v0=g*B0

The atom is then pulsed with a composite radio wave that includes the [[Relationship between frequency and energy|frequency]] v0, called the Larmor Frequency. The atom absorbs just the v0 part of the radio wave (since it is a quantum transition), and a detector in the same axis as the radio wave (usually the same antenna) is then turned on to receive any emitted energy.

Making this happen in an instrument is thus mainly an [[NMR from an Instrument point of view|engineering problem]].

From the equation above, since g is a constant for each element and B0 is a constant (it is a measure of the magnetic field strength in that instrument in the units of Tesla), there is just one frequency for that proton, which makes sense since there is just one transition, thus there is just one peak expected in the spectrum. In reality though, an atom never exists in isolation, thus it never experiences the pure B0. The actual frequency v is thus slightly different for atoms of a particular g based on the actual magnetic field around the atom. These slight differences in frequency are what gives a spectrum of peaks for a molecule rather than a single peak. There is still just one transition for that atom type (if that type is spin 1/2, such as 1H), but the transition energy is different for each 1H that is in a different magnetic environment.

If the 1H is part of a molecule then 1H atoms in the molecule in similar magnetic environments can be grouped and can be expected to give one peak per group.

To see examples, the view will be increased beyond a single 1H atom and into a collection of 1H atoms as part of molecules, such as a solution of one compound in a solvent or a pure liquid, such as ethanol.

For a sample of ethanol (CH3CH2OH), we first have to list the spin 1/2 groups in the sample:
1H and 13C

*Fortunately, the g for 1H and 13C are very different, which means that the radio frequencies needed to cause spin transitions are also different. If a narrow band of radio is used both to transmit and receive, it is possible to "see" 1H and 13C separately. In other words, when looking at 1H, the 13C will not be excited because the quantum energy is not correct. The 13C are invisible in 1H spectra, and the 1H are invisible in 13C spectra.

Next is a listing of 1H groups in the sample:

A group for the protons in the CH3 of ethanol

A group for the protons in the CH2 of ethanol

A group for the OH of ethanol.

Thus three peaks are expected in the 1H spectrum of this sample.

[[File:proton NMR of ethanol.png|500px]]

The units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity.

*Another spin 1/2 nucleus in this sample is carbon, specifically the 13C isotope. Based on the [[Table of NMR Isotopes|isotope abundance table]], 13C is only 1.11% of the total carbon atoms in a sample. The other carbon atoms have spin 0 and are not visible in NMR, so, if the instrument is sensitive enough, it can detect the 1.1% of carbons in a sample that are spin 1/2.

A list of possible 13C carbons in the sample:

A group for the CH3 of ethanol

A group for the CH2 of ethanol.

There are no other carbon sources in this sample so there should be just 2 peaks in the spectrum.

[[File:13C NMR ethanol.png|200px]]

Again, the units on the x axis are ppm, which is relative frequency, while the y axis is relative intensity. The ppm range is different than for the proton NMR spectrum because the g is different for the two nuclei, which makes the v0 different.

==Radio pulse power==
How powerful should the radio pulse be to get a good signal? Each transition requires one photon, so enough photons are needed in a pulse to cause transitions in all the nuclei in a sample. The total number of photons in a pulse of radio is the power of the pulse times the length of time that the pulse is turned on, where power is given in watts (W) and time in microseconds (µ). It is then a simple matter of running multiple experiments using different power and time settings until the maximum signal is achieved. The ideal numbers are actually limited by technical problems such as transmitter parameters and timing capabilities.

==Saturation==
Since NMR looks at quantum transitions of nuclei, only at absolute zero will all the nuclei be in the lowest energy state (not sure about that, need to check). At other temperatures there is a population in both states, with a slight excess in the lower energy state. The equation describing this is called the [[Bolztmann Distribution| Bolztmann equation]], which holds at thermal equilibrium:

(number of nuclei in the higher state)/(number of nuclei in the lower state) = e-(difference in energies/a constant*absolute temperature)

An NMR signal is only obtained when there is emission of a photon, so only the slight excess in the lower state is 'available' for excitation and subsequent emission of a photon. Thus as more and more photons are included in the pulse, at some point the populations will equalize and there will be no more transitions and no more signal. Then, as more photons are added the populations will invert, making the higher energy state slightly more populated. This will 'invert' the phase of the photons that are emitted after excitation.

==Peak Intensity==
So far there has been no discussion of how big the peaks are. Since there is one photon absorbed per nuclear transition, if photons could be counted then it would give the number of nuclei in the sample (subject to boltzmann distribution describe in the saturation section). Photon counts are represented by areas of peaks in spectra. This makes NMR a potentially quantitative method. The complication is that it is assumed that all excited nuclei release their photons at the same time so that the detector can see them. For 1H NMR this is mostly true, but for other nuclei it is not true since other factors such as delay in photon emission depending on the environment causing it to no longer be quantitative.

==Sensitivity==
Since this technique involves photon absorption by individual nuclei, the more nuclei in the sample the stronger the signal. For 1H, all protons in a natural abundance sample are 1H and thus all are available for excitation.

==Peak Splitting==
All the spins in a molecule can be considered a system, including the spins of the electrons that connect the nuclei. As a quantum system, the entire state, the state of each spin in the system, must be looked at to determine the status of the molecule at a particular time.

==Relaxation==

==Related topics==
* [[Gyromagnetic ratio]]
* [[Spins of nuclei]]
* [[Net nuclear spin]]
* [[Table of NMR Isotopes|Isotope abundance]]