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Nuclear magnetic resonance (NMR) is a
physical phenomenon
A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried W ...
in which
nuclei in a strong constant
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
are perturbed by a weak oscillating magnetic field (in the
near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
involved; in practical applications with static magnetic fields up to ca. 20
tesla, the frequency is similar to
VHF and
UHF television broadcasts
Television Broadcasts Limited (TVB) is a television broadcasting company based in Hong Kong SAR. The Company operates five free-to-air terrestrial television channels in Hong Kong, with TVB Jade as its main Cantonese language service, and TVB ...
(60–1000 MHz). NMR results from specific
magnetic
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...
properties of certain atomic nuclei.
Nuclear magnetic resonance spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic fiel ...
is widely used to determine the structure of organic molecules in solution and study
molecular physics
Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, mo ...
and
crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s as well as non-crystalline materials. NMR is also routinely used in advanced
medical imaging
Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to rev ...
techniques, such as in
magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
(MRI).
The most commonly used nuclei are and , although isotopes of many other elements, such as , can be studied by high-field NMR spectroscopy as well. In order to interact with the magnetic field in the spectrometer, the nucleus must have an intrinsic
nuclear magnetic moment
The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic dipole moment; the quadrupole moment does cause some small shifts in the hyperfine structure as ...
and
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
. This occurs when an isotope has a nonzero
nuclear spin
In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe th ...
, meaning an odd number of
protons
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
and/or
neutrons
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave ...
(see
Isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
).
Nuclide
A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state.
The word ''nuclide'' was coined by Truman ...
s with even numbers of both have a total spin of zero and are therefore NMR-inactive.
A key feature of NMR is that the
resonant
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
frequency of a particular sample substance is usually directly proportional to the strength of the applied magnetic field. It is this feature that is exploited in imaging techniques; if a sample is placed in a non-uniform magnetic field then the resonance frequencies of the sample's nuclei depend on where in the field they are located. Since the resolution of the imaging technique depends on the magnitude of the magnetic field
gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...
, many efforts are made to develop increased gradient field strength.
The principle of NMR usually involves three sequential steps:
* The alignment (polarization) of the magnetic nuclear spins in an applied, constant
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
B
0.
* The perturbation of this alignment of the nuclear spins by a weak oscillating magnetic field, usually referred to as a
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
(RF) pulse. The oscillation frequency required for significant perturbation is dependent upon the static magnetic field (B
0) and the nuclei of observation.
* The detection of the NMR signal during or after the RF pulse, due to the voltage induced in a detection coil by precession of the nuclear spins around B
0. After an RF pulse, precession usually occurs with the nuclei's intrinsic
Larmor frequency
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. The phenomenon is conceptually similar to the precession of a tilted classical gyroscope in an extern ...
and, in itself, does not involve transitions between spin states or energy levels.
The two magnetic fields are usually chosen to be
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to each other as this maximizes the NMR signal strength. The frequencies of the time-signal response by the total magnetization (M) of the nuclear spins are analyzed in
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic fiel ...
and
magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
. Both use applied magnetic fields (B
0) of great strength, often produced by large currents in
superconducting coils, in order to achieve dispersion of response frequencies and of very high homogeneity and stability in order to deliver
spectral resolution The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by \Delta\lambda, and is closely related to the resolvi ...
, the details of which are described by
chemical shift
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of ...
s, the
Zeeman effect
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
, and
Knight shift The Knight shift is a shift in the nuclear magnetic resonance (NMR) frequency of a paramagnetic
substance first published in 1949 by the UC Berkeley physicist Walter D. Knight.
For an ensemble of ''N'' spins in a magnetic induction field \vec, t ...
s (in metals). The information provided by NMR can also be increased using
hyperpolarization, and/or using two-dimensional, three-dimensional and higher-dimensional techniques.
NMR phenomena are also utilized in
low-field NMR, NMR spectroscopy and MRI in the Earth's magnetic field (referred to as
Earth's field NMR
Nuclear magnetic resonance (NMR) in the geomagnetic field is conventionally referred to as Earth's field NMR (EFNMR). EFNMR is a special case of low field NMR.
When a sample is placed in a constant magnetic field and stimulated (perturbed) by a t ...
), and in several types of
magnetometer
A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, o ...
s.
History
Nuclear magnetic resonance was first described and measured in molecular beams by
Isidor Rabi
Isidor Isaac Rabi (; born Israel Isaac Rabi, July 29, 1898 – January 11, 1988) was an American physicist who won the Nobel Prize in Physics in 1944 for his discovery of nuclear magnetic resonance, which is used in magnetic resonance im ...
in 1938, by extending the
Stern–Gerlach experiment
The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent throug ...
, and in 1944, Rabi was awarded the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
for this work. In 1946,
Felix Bloch
Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of ne ...
and
Edward Mills Purcell
Edward Mills Purcell (August 30, 1912 – March 7, 1997) was an American physicist who shared the 1952 Nobel Prize for Physics for his independent discovery (published 1946) of nuclear magnetic resonance in liquids and in solids. Nuclear magne ...
expanded the technique for use on liquids and solids, for which they shared the Nobel Prize in Physics in 1952.
Russell H. Varian filed the "Method and means for correlating nuclear properties of atoms and magnetic fields", on July 24, 1951.
Varian Associates
Varian Associates was one of the first high-tech companies in Silicon Valley. It was founded in 1948 by Russell H. and Sigurd F. Varian, William Webster Hansen, and Edward Ginzton to sell the klystron, the first vacuum tube which could amplify ...
developed the first NMR unit called NMR HR-30 in 1952.
Purcell had worked on the development of
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
during World War II at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
's
Radiation Laboratory
The Radiation Laboratory, commonly called the Rad Lab, was a microwave and radar research laboratory located at the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts. It was first created in October 1940 and operated until 31 ...
. His work during that project on the production and detection of
radio frequency power and on the absorption of such RF power by matter laid the foundation for his discovery of NMR in bulk matter.
Rabi, Bloch, and Purcell observed that magnetic nuclei, like and , could absorb RF energy when placed in a magnetic field and when the RF was of a frequency specific to the identity of the nuclei. When this absorption occurs, the nucleus is described as being ''in resonance''. Different atomic nuclei within a molecule resonate at different (radio) frequencies for the same magnetic field strength. The observation of such magnetic resonance frequencies of the nuclei present in a molecule makes it possible to determine essential chemical and structural information about the molecule.
The development of NMR as a technique in
analytical chemistry
Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separati ...
and
biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
parallels the development of electromagnetic technology and advanced
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
and their introduction into civilian use.
In 2020s it was developed the zero- to ultralow-field nuclear magnetic resonance (ZULF NMR), a form of
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
that provides abundant analytical results without the need for large
magnetic fields
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. It is combined with a special technique that makes it possible to
hyperpolarize atomic nuclei
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
.
Theory of nuclear magnetic resonance
Nuclear spin and magnets
All nucleons, that is
neutrons
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave ...
and
protons
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
, composing any atomic
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
*Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucle ...
, have the intrinsic quantum property of
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
, an intrinsic angular momentum analogous to the classical angular momentum of a spinning sphere. The overall spin of the nucleus is determined by the
spin quantum number
In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe th ...
''S''. If the numbers of both the protons and neutrons in a given
nuclide
A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state.
The word ''nuclide'' was coined by Truman ...
are even then , i.e. there is no overall spin. Then, just as electrons pair up in nondegenerate
atomic orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any spe ...
s, so do even numbers of protons or even numbers of neutrons (both of which are also
spin-1/2
In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of . The spin number describes how many symmetrical facets a particle has in one full ...
particles and hence
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s), giving zero overall spin.
However, a proton and neutron spin vector that aligns itself opposite to the external magnetic field vector will have a lower energy when their spins are parallel, not anti-parallel. This parallel spin alignment of distinguishable particles does not violate the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
. The lowering of energy for parallel spins has to do with the
quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
structure of these two nucleons. As a result, the spin ground state for the deuteron (the nucleus of
deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
, the
2H isotope of hydrogen), which has only a proton and a neutron, corresponds to a spin value of 1, ''not of zero''. On the other hand, because of the Pauli exclusion principle, the
tritium
Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive isotope of hydrogen with half-life about 12 years. The nucleus of tritium (t, sometimes called a ''triton'') contains one proton and two neutrons, whereas the nucleus o ...
isotope of hydrogen must have a pair of anti-parallel spin neutrons (of total spin zero for the neutron-spin pair), plus a proton of spin . Therefore, the tritium total nuclear spin value is again , just like for the simpler, abundant hydrogen isotope,
1H nucleus (the ''
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
''). The NMR absorption frequency for tritium is also similar to that of
1H. In many other cases of ''non-radioactive'' nuclei, the overall spin is also non-zero. For example, the nucleus has an overall spin value .
A non-zero spin
is always associated with a non-zero magnetic dipole moment,
, via the relation
where ''γ'' is the
gyromagnetic ratio
In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...
. Classically, this corresponds to the proportionality between the angular momentum and the magnetic dipole moment of a spinning charged sphere, both of which are vectors parallel to the rotation axis whose length increases proportional to the spinning frequency. It is the magnetic moment and its interaction with magnetic fields that allows the observation of NMR signal associated with transitions between nuclear spin levels during resonant RF irradiation or caused by Larmor precession of the average magnetic moment after resonant irradiation. Nuclides with even numbers of both protons and neutrons have zero
nuclear magnetic dipole moment and hence do not exhibit NMR signal. For instance, is an example of a nuclide that produces no NMR signal, whereas , , and are nuclides that do exhibit NMR spectra. The last two nuclei have spin ''S'' > 1/2 and are therefore quadrupolar nuclei.
Electron spin resonance
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spi ...
(ESR) is a related technique in which transitions between
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
ic rather than nuclear spin levels are detected. The basic principles are similar but the instrumentation, data analysis, and detailed theory are significantly different. Moreover, there is a much smaller number of molecules and materials with unpaired electron spins that exhibit ESR (or
electron paramagnetic resonance
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spin ...
(EPR)) absorption than those that have NMR absorption spectra. On the other hand, ESR has much higher signal per spin than NMR does.
Values of spin angular momentum
Nuclear
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
is an intrinsic
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
that is quantized. This means that the magnitude of this angular momentum is quantized (i.e. ''S'' can only take on a restricted range of values), and also that the x, y, and z-components of the angular momentum are quantized, being restricted to integer or half-integer multiples of ''ħ''. The integer or half-integer quantum number associated with the spin component along the z-axis or the applied magnetic field is known as the
magnetic quantum number
In atomic physics, the magnetic quantum number () is one of the four quantum numbers (the other three being the principal, azimuthal, and spin) which describe the unique quantum state of an electron. The magnetic quantum number distinguishes th ...
, ''m'', and can take values from +''S'' to −''S'', in integer steps. Hence for any given nucleus, there are a total of angular momentum states.
The ''z''-component of the angular momentum vector (
) is therefore , where ''ħ'' is the reduced
Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
. The ''z''-component of the magnetic moment is simply:
Spin energy in a magnetic field
Consider nuclei with a spin of one-half, like , or . Each nucleus has two linearly independent spin states, with ''m'' = or ''m'' = − (also referred to as spin-up and spin-down, or sometimes α and β spin states, respectively) for the z-component of spin. In the absence of a magnetic field, these states are degenerate; that is, they have the same energy. Hence the number of nuclei in these two states will be essentially equal at
thermal equilibrium
Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
.
If a nucleus is placed in a magnetic field, however, the two states no longer have the same energy as a result of the interaction between the nuclear magnetic dipole moment and the external magnetic field. The
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
of a magnetic dipole moment
in a magnetic field B
0 is given by:
Usually the ''z''-axis is chosen to be along B
0, and the above expression reduces to:
or alternatively:
As a result, the different nuclear spin states have different energies in a non-zero magnetic field. In less formal language, we can talk about the two spin states of a spin as being ''aligned'' either with or against the magnetic field. If ''γ'' is positive (true for most isotopes used in NMR) then is the lower energy state.
The energy difference between the two states is:
and this results in a small population bias favoring the lower energy state in thermal equilibrium. With more spins pointing up than down, a net spin magnetization along the magnetic field B
0 results.
Precession of the spin magnetization
A central concept in NMR is the precession of the spin magnetization around the magnetic field at the nucleus, with the angular frequency
where
relates to the oscillation frequency
and ''B'' is the magnitude of the field.
[C. Cohen-Tannoudji, B. Diu, F. Laloe, ''Quantum Mechanics'', Vol. 1, Wiley VCH, 1977.] This means that the spin magnetization, which is proportional to the sum of the spin vectors of nuclei in magnetically equivalent sites (the
expectation value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...
of the spin vector in quantum mechanics), moves on a cone around the B field. This is analogous to the precessional motion of the axis of a tilted spinning top around the gravitational field. In quantum mechanics,
is the ''Bohr frequency''
of the
and
expectation values. Precession of non-equilibrium magnetization in the applied magnetic field B
0 occurs with the Larmor frequency
without change in the populations of the energy levels because energy is constant (time-independent Hamiltonian).
Magnetic resonance and radio-frequency pulses
A perturbation of nuclear spin orientations from equilibrium will occur only when an oscillating magnetic field is applied whose frequency ''ν''
rf sufficiently closely matches the
Larmor precession
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. The phenomenon is conceptually similar to the precession of a tilted classical gyroscope in an extern ...
frequency ''ν''
L of the nuclear magnetization. The populations of the spin-up and -down energy levels then undergo
Rabi oscillations
In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, ...
,
which are analyzed most easily in terms of precession of the spin magnetization around the effective magnetic field in a reference frame rotating with the frequency ''ν''
rf.
[A. Abragam, ''The Principles of Nuclear Magnetism'', Ch. 2, Oxford Clarendon Press, 1961.] The stronger the oscillating field, the faster the Rabi oscillations or the precession around the effective field in the rotating frame. After a certain time on the order of 2–1000 microseconds, a resonant RF pulse flips the spin magnetization to the transverse plane, i.e. it makes an angle of 90° with the constant magnetic field B
0 ("90° pulse"), while after a twice longer time, the initial magnetization has been inverted ("180° pulse"). It is the transverse magnetization generated by a resonant oscillating field which is usually detected in NMR, during application of the relatively weak RF field in old-fashioned continuous-wave NMR, or after the relatively strong RF pulse in modern pulsed NMR.
Chemical shielding
It might appear from the above that all nuclei of the same nuclide (and hence the same ''γ'') would resonate at exactly the same frequency. This is not the case. The most important perturbation of the NMR frequency for applications of NMR is the "shielding" effect of the surrounding shells of electrons. Electrons, similar to the nucleus, are also charged and rotate with a spin to produce a magnetic field opposite to the applied magnetic field. In general, this electronic shielding reduces the magnetic field ''at the nucleus'' (which is what determines the NMR frequency). As a result, the frequency required to achieve resonance is also reduced. This shift in the NMR frequency due to the electronic molecular orbital coupling to the external magnetic field is called
chemical shift
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of ...
, and it explains why NMR is able to probe the chemical structure of molecules, which depends on the electron density distribution in the corresponding molecular orbitals. If a nucleus in a specific chemical group is shielded to a higher degree by a higher electron density of its surrounding molecular orbital, then its NMR frequency will be shifted "upfield" (that is, a lower chemical shift), whereas if it is less shielded by such surrounding electron density, then its NMR frequency will be shifted "downfield" (that is, a higher chemical shift).
Unless the local
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
of such molecular orbitals is very high (leading to "isotropic" shift), the shielding effect will depend on the orientation of the molecule with respect to the external field (B
0). In
solid-state NMR
Solid-state NMR (ssNMR) spectroscopy is a technique for characterizing atomic level structure in solid materials e.g. powders, single crystals and amorphous samples and tissues using nuclear magnetic resonance (NMR) spectroscopy. The anisotropic pa ...
spectroscopy,
magic angle spinning
In solid-state NMR spectroscopy, magic-angle spinning (MAS) is a technique routinely used to produce better resolution NMR spectra. MAS NMR consists in spinning the sample (usually at a frequency of 1 to 130 kHz) at the magic angle θm (ca. 5 ...
is required to average out this orientation dependence in order to obtain frequency values at the average or isotropic chemical shifts. This is unnecessary in conventional NMR investigations of molecules in solution, since rapid "molecular tumbling" averages out the
chemical shift anisotropy
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a ...
(CSA). In this case, the "average" chemical shift (ACS) or isotropic chemical shift is often simply referred to as the chemical shift.
Relaxation
The process of population relaxation refers to nuclear spins that return to thermodynamic equilibrium in the magnet. This process is also called
''T''1, "
spin-lattice" or "longitudinal magnetic" relaxation, where ''T''
1 refers to the mean time for an individual nucleus to return to its thermal equilibrium state of the spins. After the nuclear spin population has relaxed, it can be probed again, since it is in the initial, equilibrium (mixed) state.
The
precessing nuclei can also fall out of alignment with each other and gradually stop producing a signal. This is called
''T''2 or ''transverse relaxation''. Because of the difference in the actual relaxation mechanisms involved (for example, intermolecular versus intramolecular magnetic dipole-dipole interactions ), ''T''
1 is usually (except in rare cases) longer than ''T''
2 (that is, slower spin-lattice relaxation, for example because of smaller dipole-dipole interaction effects). In practice, the value of ''T''
2* which is the actually observed decay time of the observed NMR signal, or
free induction decay
In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ...
(to of the initial amplitude immediately after the resonant RF pulse), also depends on the static magnetic field inhomogeneity, which is quite significant. (There is also a smaller but significant contribution to the observed FID shortening from the RF inhomogeneity of the resonant pulse). In the corresponding FT-NMR spectrum—meaning the
Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of the
free induction decay
In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ...
—the ''T''
2* time is inversely related to the width of the NMR signal in frequency units. Thus, a nucleus with a long ''T''
2 relaxation time gives rise to a very sharp NMR peak in the FT-NMR spectrum for a very homogeneous (
"well-shimmed") static magnetic field, whereas nuclei with shorter ''T''
2 values give rise to broad FT-NMR peaks even when the magnet is shimmed well. Both ''T''
1 and ''T''
2 depend on the rate of molecular motions as well as the gyromagnetic ratios of both the resonating and their strongly interacting, next-neighbor nuclei that are not at resonance.
A
Hahn echo In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.
The ...
decay experiment can be used to measure the dephasing time, as shown in the animation. The size of the echo is recorded for different spacings of the two pulses. This reveals the decoherence that is not refocused by the 180° pulse. In simple cases, an
exponential decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
is measured which is described by the ''T''
2 time.
NMR spectroscopy
NMR spectroscopy is one of the principal techniques used to obtain physical, chemical, electronic and structural information about
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s due to the chemical shift of the resonance frequencies of the nuclear spins in the sample. Peak splittings due to
J- or dipolar couplings between nuclei are also useful. NMR spectroscopy can provide detailed and quantitative information on the functional groups, topology, dynamics and three-dimensional structure of molecules in solution and the solid state. Since the area under an NMR peak is usually proportional to the number of spins involved, peak integrals can be used to determine composition quantitatively.
Structure and molecular dynamics can be studied (with or without "magic angle" spinning (MAS)) by NMR of quadrupolar nuclei (that is, with spin ) even in the presence of magnetic "
dipole
In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways:
*An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system i ...
-dipole" interaction broadening (or simply, dipolar broadening), which is always much smaller than the quadrupolar interaction strength because it is a magnetic vs. an electric interaction effect.
Additional structural and chemical information may be obtained by performing double-quantum NMR experiments for pairs of spins or quadrupolar nuclei such as . Furthermore, nuclear magnetic resonance is one of the techniques that has been used to design quantum automata, and also build elementary
quantum computer
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
s.
[
]
Continuous-wave (CW) spectroscopy
In the first few decades of nuclear magnetic resonance, spectrometers used a technique known as
continuous-wave
A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particl ...
(CW) spectroscopy, where the transverse spin magnetization generated by a weak oscillating magnetic field is recorded as a function of the oscillation frequency or static field strength ''B''
0.
When the oscillation frequency matches the nuclear resonance frequency, the transverse magnetization is maximized and a peak is observed in the spectrum. Although NMR spectra could be, and have been, obtained using a fixed constant magnetic field and sweeping the frequency of the oscillating magnetic field, it was more convenient to use a fixed frequency source and vary the current (and hence magnetic field) in an
electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the ...
to observe the resonant absorption signals. This is the origin of the counterintuitive, but still common, "high field" and "low field" terminology for low frequency and high frequency regions, respectively, of the NMR spectrum.
As of 1996, CW instruments were still used for routine work because the older instruments were cheaper to maintain and operate, often operating at 60 MHz with correspondingly weaker (non-superconducting) electromagnets cooled with water rather than liquid helium. One radio coil operated continuously, sweeping through a range of frequencies, while another
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
coil, designed not to receive radiation from the transmitter, received signals from nuclei that reoriented in solution. As of 2014, low-end refurbished 60 MHz and 90 MHz systems were sold as FT-NMR instruments, and in 2010 the "average workhorse" NMR instrument was configured for 300 MHz.
CW spectroscopy is inefficient in comparison with
Fourier analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...
techniques (see below) since it probes the NMR response at individual frequencies or field strengths in succession. Since the NMR signal is intrinsically weak, the observed spectrum suffers from a poor
signal-to-noise ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...
. This can be mitigated by signal averaging, i.e. adding the spectra from repeated measurements. While the NMR signal is the same in each scan and so adds linearly, the
random noise
In electronics, noise is an unwanted disturbance in an electrical signal.
Noise generated by electronic devices varies greatly as it is produced by several different effects.
In particular, noise is inherent in physics, and central to the ...
adds more slowly –
proportion
Proportionality, proportion or proportional may refer to:
Mathematics
* Proportionality (mathematics), the property of two variables being in a multiplicative relation to a constant
* Ratio, of one quantity to another, especially of a part compare ...
al to the
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
E ...
of the number of spectra (see
random walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
). Hence the overall signal-to-noise ratio increases as the square-root of the number of spectra measured.
Fourier-transform spectroscopy
Most applications of NMR involve full NMR spectra, that is, the intensity of the NMR signal as a function of frequency. Early attempts to acquire the NMR spectrum more efficiently than simple CW methods involved illuminating the target simultaneously with more than one frequency. A revolution in NMR occurred when short radio-frequency pulses began to be used, with a frequency centered at the middle of the NMR spectrum. In simple terms, a short pulse of a given "carrier" frequency "contains" a range of frequencies centered about the
carrier frequency
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a m ...
, with the range of excitation (
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
) being inversely proportional to the pulse duration, i.e. the
Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of a short pulse contains contributions from all the frequencies in the neighborhood of the principal frequency. The restricted range of the NMR frequencies made it relatively easy to use short (1 - 100 microsecond) radio frequency pulses to excite the entire NMR spectrum.
Applying such a pulse to a set of nuclear spins simultaneously excites all the single-quantum NMR transitions. In terms of the net magnetization vector, this corresponds to tilting the magnetization vector away from its equilibrium position (aligned along the external magnetic field). The out-of-equilibrium magnetization vector then precesses about the external magnetic field vector at the NMR frequency of the spins. This oscillating magnetization vector
induces
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Cler ...
a voltage in a nearby pickup coil, creating an electrical signal oscillating at the NMR frequency. This signal is known as the
free induction decay
In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ...
(FID), and it contains the sum of the NMR responses from all the excited spins. In order to obtain the frequency-domain NMR
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
(NMR absorption intensity vs. NMR frequency) this time-domain signal (intensity vs. time) must be Fourier transformed. Fortunately, the development of Fourier transform (FT) NMR coincided with the development of
digital computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These pro ...
s and the digital
fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...
(FFT). Fourier methods can be applied to many types of spectroscopy.
Richard R. Ernst
Richard Robert Ernst (14 August 1933 – 4 June 2021) was a Swiss physical chemist and Nobel Laureate.
Ernst was awarded the Nobel Prize in Chemistry in 1991 for his contributions towards the development of Fourier transform nuclear magnetic re ...
was one of the pioneers of pulsed NMR and won a
Nobel Prize in chemistry
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
in 1991 for his work on Fourier Transform NMR and his development of multi-dimensional NMR spectroscopy.
Multi-dimensional NMR spectroscopy
The use of pulses of different durations, frequencies, or shapes in specifically designed patterns or ''pulse sequences'' allows production of a spectrum that contains many different types of information about the molecules in the sample. In multi-dimensional nuclear magnetic resonance spectroscopy, there are at least two pulses: one leads to the directly detected signal and the others affect the starting magnetization and spin state prior to it. The full analysis involves repeating the sequence with the pulse timings systematically varied in order to probe the oscillations of the spin system are point by point in the time domain. Multidimensional Fourier transformation of the multidimensional time signal yields the multidimensional spectrum. In
two-dimensional nuclear magnetic resonance spectroscopy Two-dimensional nuclear magnetic resonance spectroscopy (2D NMR) is a set of nuclear magnetic resonance spectroscopy (NMR) methods which give data plotted in a space defined by two frequency axes rather than one. Types of 2D NMR include correlation ...
(2D-NMR), there will be one systematically varied time period in the sequence of pulses, which will modulate the intensity or phase of the detected signals. In 3D-NMR, two time periods will be varied independently, and in 4D-NMR, three will be varied.
There are many such experiments. In some, fixed time intervals allow (among other things) magnetization transfer between nuclei and, therefore, the detection of the kinds of nuclear–nuclear interactions that allowed for the magnetization transfer. Interactions that can be detected are usually classified into two kinds. There are ''through-bond'' and ''through-space'' interactions. Through-bond interactions relate to structural connectivity of the atoms and provide information about which ones are directly connected to each other, connected by way of a single other intermediate atom, etc. Through-space interactions relate to actual geometric distances and angles, including effects of dipolar coupling and the
nuclear Overhauser effect The nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic res ...
.
Although the fundamental concept of 2D-FT NMR was proposed by
Jean Jeener
Jean Louis Charles Jeener is a Belgian physical chemist and physicist, well known for his experimental and theoretical contributions to spin thermodynamics in solids and for his invention of Two-dimensional nuclear magnetic resonance spectroscopy. ...
from the
Free University of Brussels University of Brussels may refer to several institutions in Brussels, Belgium: Current institutions
* Université libre de Bruxelles (ULB), a French-speaking university established as a separate entity in 1970
*Vrije Universiteit Brussel (VUB), a D ...
at an international conference, this idea was largely developed by
Richard Ernst, who won the 1991
Nobel prize in Chemistry
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
for his work in FT NMR, including multi-dimensional FT NMR, and especially 2D-FT NMR of small molecules. Multi-dimensional FT NMR experiments were then further developed into powerful methodologies for studying molecules in solution, in particular for the determination of the structure of
biopolymer
Biopolymers are natural polymers produced by the cells of living organisms. Like other polymers, biopolymers consist of monomeric units that are covalently bonded in chains to form larger molecules. There are three main classes of biopolymers, cl ...
s such as
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
s or even small
nucleic acid
Nucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomers made of three components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main cl ...
s.
In 2002
Kurt Wüthrich
Kurt Wüthrich (born 4 October 1938 in Aarberg, Canton of Bern) is a Swiss chemist/biophysicist and Nobel Chemistry laureate, known for developing nuclear magnetic resonance (NMR) methods for studying biological macromolecules.
Education and e ...
shared the
Nobel Prize in Chemistry
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
(with
John Bennett Fenn
John Bennett Fenn (June 15, 1917December 10, 2010) was an American professor of analytical chemistry who was awarded a share of the Nobel Prize in Chemistry in 2002. Fenn shared half of the award with Koichi Tanaka for their work in mass spectrom ...
and
Koichi Tanaka
is a Japanese electrical engineer who shared the Nobel Prize in Chemistry in 2002 for developing a novel method for mass spectrometric analyses of biological macromolecules with John Bennett Fenn and Kurt Wüthrich (the latter for work in NMR ...
) for his work with
protein FT NMR in solution.
Solid-state NMR spectroscopy
This technique complements
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
in that it is frequently applicable to molecules in an amorphous or
liquid-crystalline state, whereas crystallography, as the name implies, is performed on molecules in a crystalline phase. In electronically conductive materials, the
Knight shift The Knight shift is a shift in the nuclear magnetic resonance (NMR) frequency of a paramagnetic
substance first published in 1949 by the UC Berkeley physicist Walter D. Knight.
For an ensemble of ''N'' spins in a magnetic induction field \vec, t ...
of the resonance frequency can provide information on the mobile charge carriers. Though nuclear magnetic resonance is used to study the structure of solids, extensive atomic-level structural detail is more challenging to obtain in the solid state. Due to broadening by
chemical shift anisotropy
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a ...
(CSA) and dipolar couplings to other nuclear spins, without special techniques such as
MAS or dipolar decoupling by RF pulses, the observed spectrum is often only a broad Gaussian band for non-quadrupolar spins in a solid.
Professor Raymond Andrew at the
University of Nottingham
The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...
in the UK pioneered the development of high-resolution
solid-state nuclear magnetic resonance
Solid-state NMR (ssNMR) spectroscopy is a technique for characterizing atomic level structure in solid materials e.g. powders, single crystals and amorphous samples and tissues using nuclear magnetic resonance (NMR) spectroscopy. The anisotropic pa ...
. He was the first to report the introduction of the
MAS (magic angle sample spinning; MASS) technique that allowed him to achieve spectral resolution in solids sufficient to distinguish between chemical groups with either different chemical shifts or distinct
Knight shift The Knight shift is a shift in the nuclear magnetic resonance (NMR) frequency of a paramagnetic
substance first published in 1949 by the UC Berkeley physicist Walter D. Knight.
For an ensemble of ''N'' spins in a magnetic induction field \vec, t ...
s. In MASS, the sample is spun at several kilohertz around an axis that makes the so-called
magic angle
The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, , and so any interaction which depends on this second-order Legendre polynomial vanishes ...
''θ''
m (which is ~54.74°, where 3cos
2''θ''
m-1 = 0) with respect to the direction of the static magnetic field B
0; as a result of such magic angle sample spinning, the broad chemical shift anisotropy bands are averaged to their corresponding average (isotropic) chemical shift values. Correct alignment of the sample rotation axis as close as possible to ''θ''
m is essential for cancelling out the chemical-shift anisotropy broadening. There are different angles for the sample spinning relative to the applied field for the averaging of electric quadrupole interactions and paramagnetic interactions, correspondingly ~30.6° and ~70.1°. In amorphous materials, residual line broadening remains since each segment is in a slightly different environment, therefore exhibiting a slightly different NMR frequency.
Dipolar and
J-couplings to nearby
1H nuclei are usually removed by radio-frequency pulses applied at the
1H frequency during signal detection. The concept of cross polarization developed by Sven Hartmann and
Erwin Hahn
Erwin Louis Hahn (June 9, 1921 – September 20, 2016) was an American physicist, best known for his work on nuclear magnetic resonance (NMR).Filler, AG: The history, development, and impact of computed imaging in neurological diagnosis and neuros ...
was utilized in transferring magnetization from protons to less sensitive nuclei by M.G. Gibby,
Alex Pines and
John S. Waugh
John Stewart Waugh (April 25, 1929 – August 22, 2014) was an American chemist and Institute Professor at the Massachusetts Institute of Technology. He is known for developing average hamiltonian theory and using it to extend NMR s ...
. Then, Jake Schaefer and Ed Stejskal demonstrated the powerful use of cross polarization under MAS conditions (CP-MAS) and proton decoupling, which is now routinely employed to measure high resolution spectra of low-abundance and low-sensitivity nuclei, such as carbon-13, silicon-29, or nitrogen-15, in solids. Significant further signal enhancement can be achieved by
dynamic nuclear polarization Dynamic nuclear polarization (DNP) results from transferring spin polarization from electrons to nuclei, thereby aligning the nuclear spins to the extent that electron spins are aligned. Note that the alignment of electron spins at a given magnetic ...
from unpaired electrons to the nuclei, usually at temperatures near 110 K.
Sensitivity
Because the intensity of nuclear magnetic resonance signals and, hence, the sensitivity of the technique depends on the strength of the magnetic field the technique has also advanced over the decades with the development of more powerful magnets. Advances made in audio-visual technology have also improved the signal-generation and processing capabilities of newer instruments.
As noted above, the sensitivity of nuclear magnetic resonance signals is also dependent on the presence of a magnetically susceptible nuclide and, therefore, either on the natural abundance of such nuclides or on the ability of the experimentalist to artificially enrich the molecules, under study, with such nuclides. The most abundant naturally occurring isotopes of hydrogen and phosphorus (for example) are both magnetically susceptible and readily useful for nuclear magnetic resonance spectroscopy. In contrast, carbon and nitrogen have useful isotopes but which occur only in very low natural abundance.
Other limitations on sensitivity arise from the quantum-mechanical nature of the phenomenon. For quantum states separated by energy equivalent to radio frequencies, thermal energy from the environment causes the populations of the states to be close to equal. Since incoming radiation is equally likely to cause stimulated emission (a transition from the upper to the lower state) as absorption, the NMR effect depends on an excess of nuclei in the lower states. Several factors can reduce sensitivity, including:
* Increasing temperature, which evens out the population of states. Conversely, low temperature NMR can sometimes yield better results than room-temperature NMR, providing the sample remains liquid.
* Saturation of the sample with energy applied at the resonant radiofrequency. This manifests in both CW and pulsed NMR; in the first case (CW) this happens by using too much continuous power that keeps the upper spin levels completely populated; in the second case (pulsed), each pulse (that is at least a 90° pulse) leaves the sample saturated, and four to five times the (longitudinal) relaxation time (5''T''
1) must pass before the next pulse or pulse sequence can be applied. For single pulse experiments, shorter RF pulses that tip the magnetization by less than 90° can be used, which loses some intensity of the signal, but allows for shorter ''recycle delays''. The optimum there is called an ''Ernst angle'', after
the Nobel laureate. Especially in solid state NMR, or in samples containing very few nuclei with spin (diamond with the natural 1% of carbon-13 is especially troublesome here) the longitudinal relaxation times can be on the range of hours, while for proton-NMR they are more in the range of one second.
* Non-magnetic effects, such as electric-
quadrupole
A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...
coupling of spin-1 and spin- nuclei with their local environment, which broaden and weaken absorption peaks. , an abundant spin-1 nucleus, is difficult to study for this reason. High resolution NMR instead probes molecules using the rarer isotope, which has spin-.
Isotopes
Many isotopes of chemical elements can be used for NMR analysis.
Commonly used nuclei:
* , the most commonly used spin- nucleus in NMR investigation, has been studied using many forms of NMR. Hydrogen is highly abundant, especially in biological systems. It is the nucleus most sensitive to NMR signal (apart from , which is not commonly used due to its instability and radioactivity).
Proton NMR
Proton nuclear magnetic resonance (proton NMR, hydrogen-1 NMR, or 1H NMR) is the application of nuclear magnetic resonance in NMR spectroscopy with respect to hydrogen-1 nuclei within the molecules of a substance, in order to determine the struc ...
produces narrow chemical shift with sharp signals. Fast acquisition of quantitative results (peak integrals in stoichiometric ratio) is possible due to short relaxation time. The signal has been the sole diagnostic nucleus used for clinical
magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
(MRI).
* , a spin-1 nucleus commonly utilized as signal-free medium in the form of
deuterated solvents
Deuterated solvents are a group of compounds where one or more hydrogen atoms are substituted by deuterium atoms.
These compounds are often used in Nuclear magnetic resonance spectroscopy.
Examples
* Heavy water
* Deuterated acetone
* Deutera ...
during proton NMR, to avoid signal interference from hydrogen-containing solvents in measurement of solutes. Also used in determining the behavior of lipids in lipid membranes and other solids or liquid crystals as it is a relatively non-perturbing label which can selectively replace . Alternatively, can be detected in media specially labeled with . Deuterium resonance is commonly used in high-resolution
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic fiel ...
to monitor drifts in the magnetic field strength (lock) and to monitor the homogeneity of the external magnetic field.
* , is very sensitive to NMR. There is a very low percentage in natural helium, and subsequently has to be purified from . It is used mainly in studies of
endohedral fullerenes
Endohedral fullerenes, also called endofullerenes, are fullerenes that have additional atoms, ions, or clusters enclosed within their inner spheres. The first lanthanum C60 complex called La@C60 was synthesized in 1985. The @ (at sign) in the ...
, where its chemical inertness is beneficial to ascertaining the structure of the entrapping fullerene.
* , more sensitive than , yields sharper signals. The nuclear spin of
10B is 3 and that of
11B is . Quartz tubes must be used because
borosilicate
Borosilicate glass is a type of glass with silica and boron trioxide as the main glass-forming constituents. Borosilicate glasses are known for having very low coefficients of thermal expansion (≈3 × 10−6 K−1 at 20 °C), ma ...
glass interferes with measurement.
* spin-, is widely used, despite its relative paucity in naturally occurring carbon (approximately 1.1%). It is stable to nuclear decay. Since there is a low percentage in natural carbon, spectrum acquisition on samples which have not been experimentally enriched in takes a long time. Frequently used for labeling of compounds in synthetic and metabolic studies. Has low sensitivity and moderately wide chemical shift range, yields sharp signals. Low percentage makes it useful by preventing spin-spin couplings and makes the spectrum appear less crowded. Slow relaxation means that spectra are not integrable unless long acquisition times are used.
* , spin-1, medium sensitivity nucleus with wide chemical shift range. Its large
quadrupole
A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...
moment interferes in acquisition of high resolution spectra, limiting usefulness to smaller molecules and functional groups with a high degree of symmetry such as the headgroups of lipids.
* , spin-, relatively commonly used. Can be used for isotopically labeling compounds. Very insensitive but yields sharp signals. Low percentage in natural nitrogen together with low sensitivity requires high concentrations or expensive isotope enrichment.
* , spin-, low sensitivity and very low natural abundance (0.037%), wide chemical shift range (up to 2000 ppm). Quadrupole moment causing line broadening. Used in metabolic and biochemical studies in studies of chemical equilibria.
* , spin-, relatively commonly measured. Sensitive, yields sharp signals, has a wide chemical shift range.
* , spin-, 100% of natural phosphorus. Medium sensitivity, wide chemical shift range, yields sharp lines. Spectra tend to have a moderate amount of noise. Used in biochemical studies and in coordination chemistry with phosphorus-containing ligands.
* and , broad signal. is significantly more sensitive, preferred over despite its slightly broader signal. Organic chlorides yield very broad signals. Its use is limited to inorganic and ionic chlorides and very small organic molecules.
* , used in biochemistry to study calcium binding to DNA, proteins, etc. Moderately sensitive, very low natural abundance.
* , used in studies of
catalyst
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
s and complexes.
Other nuclei (usually used in the studies of their complexes and chemical bonding, or to detect presence of the element):
* ,
*
*
*
*
*
*
*
*
*
* , ,
*
* ,
* ,
*
*
*
*
*
* ,
*
* ,
*
*
*
*
*
*
*
*
*
*
*
*
*
* ,
*
*
*
Applications
NMR is extensively used in medicine in the form of
magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
. NMR is used in organic chemistry and industrially mainly for analysis of chemicals. The technique is also used to measure the ratio between water and fat in foods, monitor the flow of corrosive fluids in pipes, or to study molecular structures such as catalysts.
Medicine
![MRI-Philips](https://upload.wikimedia.org/wikipedia/commons/e/ee/MRI-Philips.JPG)
The application of nuclear magnetic resonance best known to the general public is
magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
for medical diagnosis and
magnetic resonance microscopy
Magnetic resonance microscopy (MRM, μMRI) is magnetic resonance imaging (MRI) at a microscopic level down to the scale of microns. The first definition of MRM was MRI having voxel resolutions of better than 100 μm.
Nomenclature
Magnetic r ...
in research settings. However, it is also widely used in biochemical studies, notably in NMR spectroscopy such as
proton NMR
Proton nuclear magnetic resonance (proton NMR, hydrogen-1 NMR, or 1H NMR) is the application of nuclear magnetic resonance in NMR spectroscopy with respect to hydrogen-1 nuclei within the molecules of a substance, in order to determine the struc ...
,
carbon-13 NMR Carbon-13 (C13) nuclear magnetic resonance (most commonly known as carbon-13 NMR spectroscopy or 13C NMR spectroscopy or sometimes simply referred to as carbon NMR) is the application of nuclear magnetic resonance (NMR) spectroscopy to carbon. It is ...
, deuterium NMR and phosphorus-31 NMR. Biochemical information can also be obtained from living tissue (e.g. human
brain
A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a v ...
tumor
A neoplasm () is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists ...
s) with the technique known as
in vivo magnetic resonance spectroscopy
In vivo magnetic resonance spectroscopy (MRS) is a specialized technique associated with magnetic resonance imaging (MRI).
Magnetic resonance spectroscopy (MRS), also known as nuclear magnetic resonance (NMR) spectroscopy, is a non-invasive, io ...
or
chemical shift
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of ...
NMR microscopy.
These spectroscopic studies are possible because nuclei are surrounded by orbiting electrons, which are charged particles that generate small, local magnetic fields that add to or subtract from the external magnetic field, and so will partially shield the nuclei. The amount of shielding depends on the exact local environment. For example, a hydrogen bonded to an
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
will be shielded differently from a hydrogen bonded to a carbon atom. In addition, two hydrogen nuclei can interact via a process known as
spin-spin coupling
In quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling. For instance, the orbit and spin of a single particle can interact th ...
, if they are on the same molecule, which will split the lines of the spectra in a recognizable way.
As one of the two major spectroscopic techniques used in
metabolomics
Metabolomics is the scientific study of chemical processes involving metabolites, the small molecule substrates, intermediates, and products of cell metabolism. Specifically, metabolomics is the "systematic study of the unique chemical fingerprin ...
, NMR is used to generate metabolic fingerprints from biological fluids to obtain information about disease states or toxic insults.
Chemistry
By studying the peaks of nuclear magnetic resonance spectra, chemists can determine the structure of many compounds. It can be a very selective technique, distinguishing among many atoms within a molecule or collection of molecules of the same type but which differ only in terms of their local chemical environment. NMR spectroscopy is used to unambiguously identify known and novel compounds, and as such, is usually required by scientific journals for identity confirmation of synthesized new compounds. See the articles on
carbon-13 NMR Carbon-13 (C13) nuclear magnetic resonance (most commonly known as carbon-13 NMR spectroscopy or 13C NMR spectroscopy or sometimes simply referred to as carbon NMR) is the application of nuclear magnetic resonance (NMR) spectroscopy to carbon. It is ...
and
proton NMR
Proton nuclear magnetic resonance (proton NMR, hydrogen-1 NMR, or 1H NMR) is the application of nuclear magnetic resonance in NMR spectroscopy with respect to hydrogen-1 nuclei within the molecules of a substance, in order to determine the struc ...
for detailed discussions.
A chemist can determine the identity of a compound by comparing the observed nuclear precession frequencies to known frequencies. Further structural data can be
elucidated by observing ''
spin-spin coupling
In quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling. For instance, the orbit and spin of a single particle can interact th ...
'', a process by which the precession frequency of a nucleus can be influenced by the spin orientation of a chemically bonded nucleus. Spin-spin coupling is easily observed in NMR of hydrogen-1 ( NMR) since its natural abundance is nearly 100%.
Because the nuclear magnetic resonance ''timescale'' is rather slow, compared to other spectroscopic methods, changing the temperature of a ''T''
2* experiment can also give information about fast reactions, such as the
Cope rearrangement
The Cope rearrangement is an extensively studied organic reaction involving the ,3sigmatropic rearrangement of 1,5-dienes. It was developed by Arthur C. Cope and Elizabeth Hardy. For example, 3-methyl-hexa-1,5-diene heated to 300 °C yields ...
or about structural dynamics, such as ring-flipping in
cyclohexane
Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colorless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
. At low enough temperatures, a distinction can be made between the axial and equatorial hydrogens in cyclohexane.
An example of nuclear magnetic resonance being used in the determination of a structure is that of
buckminsterfullerene
Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a soccer ball. Each of its 60 carbon atoms is bonded ...
(often called "buckyballs", composition C
60). This now famous form of carbon has 60 carbon atoms forming a sphere. The carbon atoms are all in identical environments and so should see the same internal H field. Unfortunately, buckminsterfullerene contains no hydrogen and so nuclear magnetic resonance has to be used. spectra require longer acquisition times since carbon-13 is not the common isotope of carbon (unlike hydrogen, where is the common isotope). However, in 1990 the spectrum was obtained by R. Taylor and co-workers at the
University of Sussex
, mottoeng = Be Still and Know
, established =
, type = Public research university
, endowment = £14.4 million (2020)
, budget = £319.6 million (2019–20)
, chancellor = Sanjeev Bhaskar
, vice_chancellor = Sasha Roseneil
, ...
and was found to contain a single peak, confirming the unusual structure of buckminsterfullerene.
Purity determination (w/w NMR)
While NMR is primarily used for structural determination, it can also be used for purity determination, provided that the structure and
molecular weight
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
of the compound is known. This technique requires the use of an
internal standard An internal standard in analytical chemistry is a chemical substance that is added in a constant amount to samples, the blank and calibration standards in a chemical analysis. This substance can then be used for calibration by plotting the ratio of ...
of known purity. Typically this standard will have a high molecular weight to facilitate accurate weighing, but relatively few protons so as to give a clear peak for later integration e.g.
1,2,4,5-tetrachloro-3-nitrobenzene. Accurately weighed portions of the standard and sample are combined and analysed by NMR. Suitable peaks from both compounds are selected and the purity of the sample is determined via the following equation.
:
Where:
* ''w''
std: weight of internal standard
* ''w''
spl: weight of sample
* ''n''
sub>std: the integrated area of the peak selected for comparison in the standard, corrected for the number of protons in that
functional group
In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...
* ''n''
sub>spl: the integrated area of the peak selected for comparison in the sample, corrected for the number of protons in that
functional group
In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...
* ''MW''
std:
molecular weight
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
of standard
* ''MW''
spl:
molecular weight
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
of sample
* ''P'': purity of internal standard
Non-destructive testing
Nuclear magnetic resonance is extremely useful for analyzing samples non-destructively. Radio-frequency magnetic fields easily penetrate many types of matter and anything that is not highly conductive or inherently
ferromagnetic
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
. For example, various expensive biological samples, such as
nucleic acids
Nucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomers made of three components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main clas ...
, including
RNA
Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
and
DNA, or
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
s, can be studied using nuclear magnetic resonance for weeks or months before using destructive biochemical experiments. This also makes nuclear magnetic resonance a good choice for analyzing dangerous samples.
Segmental and molecular motions
In addition to providing static information on molecules by determining their 3D structures, one of the remarkable advantages of NMR over
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
is that it can be used to obtain important dynamic information. This is due to the orientation dependence of the chemical-shift, dipole-coupling, or electric-quadrupole-coupling contributions to the instantaneous NMR frequency in an anisotropic molecular environment. When the molecule or segment containing the NMR-observed nucleus changes its orientation relative to the external field, the NMR frequency changes, which can result in changes in one- or two-dimensional spectra or in the relaxation times, depending on the correlation time and amplitude of the motion.
Data acquisition in the petroleum industry
Another use for nuclear magnetic resonance is
data acquisition Data acquisition is the process of sampling signals that measure real-world physical conditions and converting the resulting samples into digital numeric values that can be manipulated by a computer. Data acquisition systems, abbreviated by the acro ...
in the
petroleum industry
The petroleum industry, also known as the oil industry or the oil patch, includes the global processes of exploration, extraction, refining, transportation (often by oil tankers and pipelines), and marketing of petroleum products. The larges ...
for
petroleum
Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crud ...
and
natural gas
Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbo ...
exploration and recovery. Initial research in this domain began in the 1950s, however, the first commercial instruments were not released until the early 1990s. A
borehole
A borehole is a narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water ( drilled water well and tube well), other liquids (such as petro ...
is drilled into rock and sedimentary strata into which nuclear magnetic resonance logging equipment is lowered. Nuclear magnetic resonance analysis of these boreholes is used to measure rock porosity, estimate permeability from pore size distribution and identify pore fluids (water, oil and gas). These instruments are typically
low field NMR
Low field NMR spans a range of different nuclear magnetic resonance (NMR) modalities, going from NMR conducted in permanent magnets, supporting magnetic fields of a few tesla (unit), tesla (T), all the way down to zero field NMR, where the Earth's ...
spectrometers.
NMR logging, a subcategory of electromagnetic logging, measures the induced magnet moment of hydrogen nuclei (protons) contained within the fluid-filled pore space of porous media (reservoir rocks). Unlike conventional logging measurements (e.g., acoustic, density, neutron, and resistivity), which respond to both the rock matrix and fluid properties and are strongly dependent on mineralogy, NMR-logging measurements respond to the presence of hydrogen. Because hydrogen atoms primarily occur in pore fluids, NMR effectively responds to the volume, composition, viscosity, and distribution of these fluids, for example oil, gas or water. NMR logs provide information about the quantities of fluids present, the properties of these fluids, and the sizes of the pores containing these fluids. From this information, it is possible to infer or estimate:
* The volume (porosity) and distribution (permeability) of the rock pore space
* Rock composition
* Type and quantity of fluid hydrocarbons
* Hydrocarbon producibility
The basic core and log measurement is the ''T''
2 decay, presented as a distribution of ''T''
2 amplitudes versus time at each sample depth, typically from 0.3 ms to 3 s. The ''T''
2 decay is further processed to give the total pore volume (the total porosity) and pore volumes within different ranges of ''T''
2. The most common volumes are the bound fluid and free fluid. A permeability estimate is made using a transform such as the Timur-Coates or SDR permeability transforms. By running the log with different acquisition parameters, direct hydrocarbon typing and enhanced diffusion are possible.
Flow probes for NMR spectroscopy
![NMR Stopped Flow Probe](https://upload.wikimedia.org/wikipedia/commons/d/da/NMR_Stopped_Flow_Probe.png)
Recently, real-time applications of NMR in liquid media have been developed using specifically designed flow probes (flow cell assemblies) which can replace standard tube probes. This has enabled techniques that can incorporate the use of
high performance liquid chromatography
High-performance liquid chromatography (HPLC), formerly referred to as high-pressure liquid chromatography, is a technique in analytical chemistry used to separate, identify, and quantify each component in a mixture. It relies on pumps to pa ...
(HPLC) or other continuous flow sample introduction devices. These flow probes have used in various online process monitoring such as chemical reactions, environmental pollutant degradation.
Process control
NMR has now entered the arena of real-time
process control
An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. I ...
and
process optimization
Process optimization is the discipline of adjusting a process so as to optimize (make the best or most effective use of) some specified set of parameters without violating some constraint. The most common goals are minimizing cost and maximizing ...
in
oil refineries
An oil refinery or petroleum refinery is an industrial process plant where petroleum (crude oil) is transformed and refined into useful products such as gasoline (petrol), diesel fuel, asphalt base, fuel oils, heating oil, kerosene, liquefie ...
and
petrochemical
Petrochemicals (sometimes abbreviated as petchems) are the chemical products obtained from petroleum by refining. Some chemical compounds made from petroleum are also obtained from other fossil fuels, such as coal or natural gas, or renewable sou ...
plants. Two different types of NMR analysis are utilized to provide real time analysis of feeds and products in order to control and optimize unit operations. Time-domain NMR (TD-NMR) spectrometers operating at low field (2–20 MHz for ) yield
free induction decay
In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ...
data that can be used to determine absolute
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
content values,
rheological
Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appli ...
information, and component composition. These spectrometers are used in
mining
Mining is the extraction of valuable minerals or other geological materials from the Earth, usually from an ore body, lode, vein, seam, reef, or placer deposit. The exploitation of these deposits for raw material is based on the economic via ...
,
polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
production,
cosmetics
Cosmetics are constituted mixtures of chemical compounds derived from either natural sources, or synthetically created ones. Cosmetics have various purposes. Those designed for personal care and skin care can be used to cleanse or protect ...
and food manufacturing as well as
coal
Coal is a combustible black or brownish-black sedimentary rock, formed as rock strata called coal seams. Coal is mostly carbon with variable amounts of other elements, chiefly hydrogen, sulfur, oxygen, and nitrogen.
Coal is formed when dea ...
analysis. High resolution FT-NMR spectrometers operating in the 60 MHz range with shielded permanent magnet systems yield high resolution NMR spectra of
refinery
A refinery is a production facility composed of a group of chemical engineering unit processes and unit operations refining certain materials or converting raw material into products of value.
Types of refineries
Different types of refineries ...
and
petrochemical
Petrochemicals (sometimes abbreviated as petchems) are the chemical products obtained from petroleum by refining. Some chemical compounds made from petroleum are also obtained from other fossil fuels, such as coal or natural gas, or renewable sou ...
streams. The variation observed in these spectra with changing physical and chemical properties is modeled using
chemometrics
Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, a ...
to yield predictions on unknown samples. The prediction results are provided to
control systems
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...
via analogue or digital outputs from the spectrometer.
Earth's field NMR
In the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
, NMR frequencies are in the
audio frequency
An audio frequency or audible frequency (AF) is a periodic vibration whose frequency is audible to the average human. The SI unit of frequency is the hertz (Hz). It is the property of sound that most determines pitch.
The generally accepted ...
range, or the
very low frequency
Very low frequency or VLF is the ITU designation for radio frequencies (RF) in the range of 3–30 kHz, corresponding to wavelengths from 100 to 10 km, respectively. The band is also known as the myriameter band or myriameter wave a ...
and
ultra low frequency
Ultra low frequency (ULF) is the ITU designation for the frequency range of electromagnetic waves between 300 hertz and 3 kilohertz, corresponding to wavelengths between 1,000 to 100 km. In magnetosphere science and seismology, alternative defin ...
bands of the
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
spectrum. Earth's field NMR (EFNMR) is typically stimulated by applying a relatively strong dc magnetic field pulse to the sample and, after the end of the pulse, analyzing the resulting low frequency alternating magnetic field that occurs in the Earth's magnetic field due to
free induction decay
In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ...
(FID). These effects are exploited in some types of
magnetometer
A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, o ...
s, EFNMR spectrometers, and MRI imagers. Their inexpensive portable nature makes these instruments valuable for field use and for teaching the principles of NMR and MRI.
An important feature of EFNMR spectrometry compared with high-field NMR is that some aspects of molecular structure can be observed more clearly at low fields and low frequencies, whereas other aspects observable at high fields are not observable at low fields. This is because:
* Electron-mediated heteronuclear
''J''-couplings (
spin-spin coupling
In quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling. For instance, the orbit and spin of a single particle can interact th ...
s) are field independent, producing clusters of two or more frequencies separated by several Hz, which are more easily observed in a fundamental resonance of about 2 kHz."Indeed it appears that enhanced resolution is possible due to the long spin relaxation times and high field homogeneity which prevail in EFNMR."
* Chemical shifts of several
ppm are clearly separated in high field NMR spectra, but have separations of only a few millihertz at proton EFNMR frequencies, so are usually not resolved.
Zero field NMR
In
zero field NMR
Zero- to ultralow-field (ZULF) NMR is the acquisition of nuclear magnetic resonance (NMR) spectra of chemicals with magnetically active nuclei ( spins 1/2 and greater) in an environment carefully screened from magnetic fields (including from the ...
all magnetic fields are shielded such that magnetic fields below 1 nT (nano
tesla) are achieved and the nuclear precession frequencies of all nuclei are close to zero and indistinguishable. Under those circumstances the observed spectra are no-longer dictated by chemical shifts but primarily by ''J''-coupling interactions which are independent of the external magnetic field. Since inductive detection schemes are not sensitive at very low frequencies, on the order of the ''J''-couplings (typically between 0 and 1000 Hz), alternative detection schemes are used. Specifically, sensitive
magnetometer
A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, o ...
s turn out to be good detectors for zero field NMR. A zero magnetic field environment does not provide any polarization hence it is the combination of zero field NMR with hyperpolarization schemes that makes zero field NMR desirable.
Quantum computing
NMR
quantum computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
uses the
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
states of nuclei within molecules as
qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
s. NMR differs from other implementations of quantum computers in that it uses an
ensemble
Ensemble may refer to:
Art
* Architectural ensemble
* ''Ensemble'' (album), Kendji Girac 2015 album
* Ensemble (band), a project of Olivier Alary
* Ensemble cast (drama, comedy)
* Ensemble (musical theatre), also known as the chorus
* ''En ...
of systems; in this case, molecules.
Magnetometers
Various magnetometers use NMR effects to measure magnetic fields, including
proton precession magnetometers (PPM) (also known as
proton magnetometer
A proton magnetometer, also known as a proton precession magnetometer (PPM), uses the principle of Earth's field nuclear magnetic resonance (EFNMR) to measure very small variations in the Earth's magnetic field, allowing ferrous objects on land ...
s), and
Overhauser magnetometers.
SNMR
Surface magnetic resonance (or magnetic resonance sounding) is based on the principle of nuclear magnetic resonance (NMR) and measurements can be used to indirectly estimate the water content of saturated and unsaturated zones in the earth's subsurface.
[Anatoly Legtchenko(2013)Magnetic Resonance Imaging for Groundwater wiley, New york city] SNMR is used to estimate aquifer properties, including quantity of water contained in the
aquifer
An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characterist ...
,
porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
, and
hydraulic conductivity
Hydraulic conductivity, symbolically represented as (unit: m/s), is a property of porous materials, soils and rocks, that describes the ease with which a fluid (usually water) can move through the pore space, or fractures network. It depends on th ...
.
Makers of NMR equipment
Major NMR instrument makers include
Thermo Fisher Scientific
Thermo Fisher Scientific Inc. is an American supplier of scientific instrumentation, reagents and consumables, and software services. Based in Waltham, Massachusetts, Thermo Fisher was formed through the merger of Thermo Electron and Fisher S ...
,
Magritek Magritek is a scientific instrument company based in Wellington, New Zealand, and Aachen, Germany, that was established in 2004 and specialises in compact, portable and benchtop nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) ...
,
Oxford Instruments
Oxford Instruments plc is a United Kingdom manufacturing and research company that designs and manufactures tools and systems for industry and research. The company is headquartered in Abingdon, Oxfordshire, England, with sites in the United Ki ...
,
Bruker
Bruker Corporation is an American manufacturer of scientific instruments for molecular and materials research, as well as for industrial and applied analysis. It is headquartered in Billerica, Massachusetts, and is the publicly traded parent compa ...
,
Spinlock SRL
Spinlock is a technology based company specialized in the manufacture and development of nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) equipment.
History
Spinlock was founded in 2003 by Dr. Daniel J. Pusiol, a renowned ...
,
General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable energ ...
,
JEOL
is a major developer and manufacturer of electron microscopes and other scientific instruments, industrial equipment and medical equipment.
Its headquarters are in Tokyo, Japan, with 25 domestic and foreign subsidiaries and associated companies ...
,
Kimble Chase
Kimble Chase, short for Kimble Chase Life Science and Research Products LLC, is headquartered in Vineland, New Jersey. Kimble Chase supplies laboratory equipment and consumables for analytical chemists in the pharmaceutical, scientific, clinical, ...
,
Philips
Koninklijke Philips N.V. (), commonly shortened to Philips, is a Dutch multinational conglomerate corporation that was founded in Eindhoven in 1891. Since 1997, it has been mostly headquartered in Amsterdam, though the Benelux headquarters i ...
,
Siemens AG
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
, and formerly
Agilent Technologies, Inc.
Agilent Technologies, Inc. is an American life sciences company that provides instruments, software, services, and consumables for the entire laboratory workflow. Its global headquarters is located in Santa Clara, California. Agilent was establi ...
(who acquired
Varian, Inc.
Varian, Inc. was one of the largest manufacturers of scientific instruments for the scientific industry. They had offerings over a broad range of chemical analysis equipment, with a particular focus on Information Rich Detection and Vacuum tech ...
).
See also
*
Benchtop NMR spectrometer
A Benchtop nuclear magnetic resonance spectrometer (Benchtop NMR spectrometer) refers to a Fourier transform nuclear magnetic resonance (FT-NMR) spectrometer that is significantly more compact and portable than the conventional equivalents, such th ...
*
Larmor equation
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. The phenomenon is conceptually similar to the precession of a tilted classical gyroscope in an extern ...
(Not to be confused with
Larmor formula
In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light.
When any charged ...
).
*
Least-squares spectral analysis
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally ...
*
Liquid nitrogen
Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wide ...
*
NMR crystallography Nuclear magnetic resonance crystallography (NMR crystallography) is a method which utilizes primarily NMR spectroscopy to determine the structure of solid materials on the atomic scale. Thus, solid-state NMR spectroscopy would be used primarily, po ...
*
NMR spectra database
A nuclear magnetic resonance spectra database is an electronic repository of information concerning Nuclear magnetic resonance (NMR) spectra. Such repositories can be downloaded as self-contained data sets or used online. The form in which the ...
*
Nuclear magnetic resonance in porous media Nuclear magnetic resonance (NMR) in porous materials covers the application of using NMR as a tool to study the structure of porous media and various processes occurring in them. This technique allows the determination of characteristics such as the ...
*
Nuclear quadrupole resonance Nuclear quadrupole resonance spectroscopy or NQR is a chemical analysis technique related to nuclear magnetic resonance ( NMR). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a magnetic field, and for this reason NQR spectro ...
(NQR)
*
Protein dynamics Proteins are generally thought to adopt unique structures determined by their amino acid sequences. However, proteins are not strictly static objects, but rather populate ensembles of (sometimes similar) conformations. Transitions between these stat ...
*
Rabi cycle
In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, ...
*
Relaxometry Relaxometry refers to the study and/or measurement of Relaxation (NMR), relaxation variables in Nuclear magnetic resonance, Nuclear Magnetic Resonance and Magnetic Resonance Imaging. In Nuclear magnetic resonance, NMR, nuclear magnetic moments are u ...
*
Spin echo In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.
The NMR ...
*
Structure-based assignment
References
Further reading
*
*
* K.V.R. Chary,
Girjesh Govil
Girjesh Govil (25 September 1940 – 12 October 2021) was an Indian molecular biophysicist and a Raja Ramanna professor at the Tata Institute of Fundamental Research. He was known for his researches on semi-empirical quantum chemical theories. ...
(2008) ''NMR in Biological Systems: From Molecules to Human.'' Springer. .
*
*
The Feynman Lectures on Physics Vol. II Ch. 35: Paramagnetism and Magnetic Resonance*
*
*
*
*
*
*
*
*
*
External links
Tutorial
NMR Concepts
NMR Course Notes
Animations and simulations
This animation shows a spin, the modification of spin with magnetic field and HF pulse, spin echo sequences, inversion recovery sequence, gradient echo sequence and relaxation of spin
Video
introduction to NMR and MRIRichard Ernst, NL – Developer of multidimensional NMR techniquesFreeview video provided by the Vega Science Trust.
'An Interview with Kurt Wuthrich'Freeview video by the Vega Science Trust (Wüthrich was awarded a Nobel Prize in Chemistry in 2002 "for his development of nuclear magnetic resonance spectroscopy for determining the three-dimensional structure of biological macromolecules in solution").
; Other
*
Spotlight on nuclear magnetic resonance: a timeless technique
{{DEFAULTSORT:Nuclear Magnetic Resonance
Scientific techniques
Articles containing video clips
Biomagnetics