Nuclear magnetic resonance ( NMR ) is the resonant absorption or emission of electromagnetic energy by a substance containing nuclei with nonzero spin in an external magnetic field at frequency ν (called the NMR frequency), due to the reorientation of the magnetic moments of the nuclei.
The phenomenon of nuclear magnetic resonance was discovered in 1938 by Isidor Rabi in molecular beams, for which he was awarded the Nobel Prize in 1944 [1] . In 1946, Felix Bloch and Edward Mills Purcell obtained nuclear magnetic resonance in liquids and solids (Nobel Prize 1952) [2] [3] .
The same atomic nuclei in different environments in a molecule show different NMR signals. The difference between the NMR signal and the signal of a standard substance allows us to determine the so-called chemical shift , which is caused by the chemical structure of the substance under study. In NMR techniques, there are many opportunities to determine the chemical structure of substances, the conformation of molecules, the effects of mutual influence, intramolecular transformations.
Content
NMR physics
The phenomenon of nuclear magnetic resonance is based on the magnetic properties of atomic nuclei with non - zero spin (proper rotational moment ).
All cores carry an electrical charge. In most types of nuclei, this charge "rotates" relative to the axis of the nucleus, and this rotation of the nuclear charge generates a magnetic dipole moment , which is able to interact with an external magnetic field. Among all nuclei, only nuclei containing simultaneously an even number of neutrons and an even number of protons (even-even nuclei), in the ground state, do not possess a torque, and consequently, a dipole magnetic moment. The rest of the cores have a non-zero torque in the ground state. associated with the magnetic moment by ratio
- ,
Where - Planck's constant - spin quantum number, - gyromagnetic ratio .
The angular momentum and the magnetic moment of the nucleus are quantized, and the eigenvalues of the projection and the angular and magnetic moments on the z axis of an arbitrarily chosen coordinate system are determined by the relation
- and ,
Where - The magnetic quantum number of the proper state of the nucleus. Meanings determined by the spin quantum number of the nucleus
- ,
that is, the core may be in states.
So, the proton (or other nucleus with I = 1/2 - 13 C, 19 F, 31 P, etc.) can only be in two states
Such a nucleus can be represented as a magnetic dipole , the z- component of which can be oriented parallel to or antiparallel to the positive direction of the z axis of an arbitrary coordinate system.
The core is 6 Li (or another core with I = 1 - 14 N, 32 P, etc.) can be in three states
It should be noted that in the absence of an external magnetic field, all states with different have the same energy, that is, are degenerate. The degeneracy is lifted in an external magnetic field, and the splitting with respect to the degenerate state is proportional to the magnitude of the external magnetic field and magnetic moment of the state and for a nucleus with a spin quantum number I in an external magnetic field a system of 2 I + 1 energy levels appears that is, nuclear magnetic resonance is of the same nature as the Zeeman effect of splitting electronic levels in a magnetic field.
In the simplest case, for a nucleus with a spin with I = 1/2 - for example, for a proton, - splitting
and the difference in the energy of spin states
This expression simply states that the energy difference proportional to , since the other values are constants. For a magnetic field of the order of 1 T and a typical nuclear magnetic moment, the splitting of the levels is in the energy range corresponding to the frequencies of the electromagnetic field lying in the radio band.
As soon as a system of two levels has arisen, it is possible to introduce energy in the form of radio frequency radiation with a frequency ( ) to excite transitions between these energy levels in a constant magnetic field . The fundamental NMR equation relating the applied frequency ( ) with the magnitude of the magnetic field is written as
insofar as
Exposure frequency is in the megahertz range (MHz). For protons with a field size equal to 2.35 T , the irradiation frequency is 100 MHz . As the field increases n times, the resonance frequency also increases. When the ratio of frequency and field, equal to The system is in resonance; the proton absorbs energy, goes to a higher energy level, and you can record the spectrum. Hence the name of nuclear magnetic resonance spectroscopy. Constant called the gyromagnetic ratio and is the fundamental nuclear constant. This is the proportionality factor between the magnetic moment. and spin the nucleus :
.
Radio frequency energy can be entered either in the continuous sweep mode in a certain frequency range (continuous wave (CW) or continuous mode), or in the form of a short radio frequency pulse containing the entire set of frequencies (pulse mode). These two methods correspond to two different types of NMR spectrometers.
An ensemble of equivalent protons precessing with a random phase around the z axis (i.e. around the direction of a constant magnetic field ), generates a total macroscopic magnetization in the direction of the z axis, but not in the xy plane.
The problem is how to apply radio-frequency electromagnetic energy to protons oriented in a constant magnetic field, and how then to measure the energy absorbed by the protons during the transition to a higher spin state. This can be ascertained in terms of classical mechanics, if the proton is represented as a particle rotating in an external magnetic field. The proton magnetic axis precesses around the z axis of a constant magnetic field. just as a top is precessing under the action of gravity, the axis of rotation of which is deflected from the perpendicular.
When the frequency of the applied high-frequency field ( ) is equal to the precession frequency of equivalent protons (called the Larmor frequency in classical physics , in MHz), nuclear magnetic resonance state is achieved, and the basic NMR equation can be written as
This equation applies to an ensemble of isolated protons.
The observation of NMR is facilitated by the fact that in most substances the atoms do not possess constant magnetic moments of the electrons of the atomic shells due to the freezing effect of the orbital moment .
The resonance NMR frequencies in metals are higher than in diamagnets ( Knight shift ).
Chemical polarization of nuclei
When some chemical reactions take place in a magnetic field, the NMR spectra of the reaction products show either an abnormally large absorption or radio emission. This fact indicates the non-equilibrium population of the nuclear Zeeman levels in the molecules of the reaction products. Excessive occupancy of the lower level is accompanied by anomalous absorption. Inverse population (the upper level is populated more than the lower) leads to radio emission. This phenomenon is called chemical polarization of nuclei .
Larmor frequencies of some atomic nuclei
core | Larmor frequency in MHz at 0.5 Tesla | Larmor frequency in MHz with 1 Tesla | Larmor frequency in MHz at 7.05 Tesla |
---|---|---|---|
1 H ( Hydrogen ) | 21.29 | 42,58 | 300.18 |
2 D ( Deuterium ) | 3.27 | 6.53 | 46.08 |
13 C ( Carbon ) | 5.36 | 10.71 | 75.51 |
23 Na ( Sodium ) | 5.63 | 11.26 | 79.40 |
39 K ( Potassium ) | 1.00 | 1.99 |
The frequency for the resonance of protons is in the range of short waves (wavelength of about 7 m) [4] .
NMR Application
Spectroscopy
Instruments
The heart of the NMR spectrometer is a powerful magnet . In the experiment, first carried out in practice by Purcell , a sample placed in a glass ampoule with a diameter of about 5 mm is placed between the poles of a strong electromagnet. Then, in order to improve the uniformity of the magnetic field, the ampoule begins to rotate, and the magnetic field acting on it gradually increases. A high- quality radio-frequency generator is used as a radiation source. Under the action of an amplifying magnetic field, the nuclei to which the spectrometer is tuned begin to resonate. In this case, shielded nuclei resonate at a frequency slightly lower than the nuclei lacking electron shells. Energy absorption is recorded by a radio frequency bridge and then recorded by a recorder. The frequency is increased until it reaches a certain limit, above which resonance is impossible.
Since the currents coming from the bridge are very small, they do not limit themselves to removing one spectrum, but make several dozen passes. All received signals are summarized in the final graph, the quality of which depends on the signal-to-noise ratio of the device.
In this method, the sample is subjected to radio frequency radiation at a constant frequency, while the strength of the magnetic field changes, so it is also called the method of continuous irradiation (CW, continous wave).
The traditional method of NMR spectroscopy has many drawbacks. First, it takes a lot of time to build each spectrum. Secondly, it is very demanding of the absence of external interference, and as a rule, the spectra obtained have significant noise. Thirdly, it is unsuitable for creating high frequency spectrometers (300, 400, 500 and more MHz ). Therefore, modern NMR instruments use the so-called pulse spectroscopy (PW) method based on the Fourier transform of the received signal. Currently, all NMR spectrometers are built on the basis of powerful superconducting magnets with a constant magnetic field.
In contrast to the CW method, in the pulsed version, the excitation of nuclei is carried out not by a “constant wave”, but by means of a short pulse of several microseconds duration. The amplitudes of the frequency components of the pulse decrease with increasing distance from ν 0 . But since it is desirable that all the nuclei are irradiated in the same way, it is necessary to use “hard pulses”, that is, short pulses of high power. The duration of the pulse is chosen so that the width of the frequency band is one or two orders of magnitude wider than the width of the spectrum. Power reaches several thousand watts .
As a result of pulse spectroscopy, it is not the usual spectrum with visible resonance peaks, but the image of damped resonance oscillations in which all signals from all resonant nuclei are mixed — the so-called “ free induction decay ” (FID, free induction decay ) are mixed. To transform a given spectrum, mathematical methods are used, the so-called Fourier transform , according to which any function can be represented as the sum of a set of harmonic oscillations .
NMR spectra
For qualitative analysis using NMR, spectral analysis is used based on such remarkable properties of this method:
- the signals of atomic nuclei entering into certain functional groups lie in strictly defined parts of the spectrum;
- the integral area bounded by the peak is strictly proportional to the number of resonating atoms;
- nuclei lying through 1-4 connections are capable of producing multiplet signals as a result of so-called. splitting each other.
The position of the signal in the NMR spectra is characterized by their chemical shift relative to the reference signal. As the latter, tetramethylsilane Si (CH 3 ) 4 (TMS) is used in NMR 1 H and 13 C. The unit of chemical shift is the millionth part (ppm) of the frequency of the instrument. If we take the TMS signal as 0, and the signal shift in a weak field is considered a positive chemical shift, then we get the so-called δ scale. If the resonance of tetramethylsilane equate 10 ppm and to reverse the signs, the resulting scale will be the τ scale, which is practically not used at present. If the spectrum of a substance is too complicated to interpret, one can use quantum chemical methods for calculating the screening constants and, based on them, correlate the signals.
NMR introscopy
The phenomenon of nuclear magnetic resonance can be applied not only in physics and chemistry , but also in medicine : the human body is a combination of the same organic and inorganic molecules.
To observe this phenomenon, the object is placed in a constant magnetic field and exposed to radio frequency and gradient magnetic fields. A variable electromotive force (EMF) arises in the inductance coil surrounding the object under study, whose amplitude-frequency spectrum and transient characteristics carry information about the spatial density of resonant atomic nuclei, as well as other parameters specific to nuclear magnetic resonance. Computer processing of this information forms a three-dimensional image that characterizes the density of chemically equivalent nuclei, the relaxation times of nuclear magnetic resonance , the distribution of flow rates, the diffusion of molecules, and the biochemical metabolic processes in living tissues.
The essence of NMR introscopy (or magnetic resonance imaging ) consists, in essence, in the implementation of a special kind of quantitative analysis of the amplitude of a nuclear magnetic resonance signal. In conventional NMR spectroscopy, they strive to realize, if possible, the best resolution of the spectral lines. To this end, the magnetic systems are adjusted in such a way that within the sample to create the best possible field uniformity. In the methods of NMR introscopy, on the contrary, the magnetic field is created deliberately inhomogeneous. Then there is reason to expect that the frequency of nuclear magnetic resonance at each point of the sample has its own value, which differs from the values in other parts. By specifying any code for the amplitude gradations of the NMR signals (brightness or color on the monitor screen), it is possible to obtain a conditional image ( tomogram ) of slices of the internal structure of the object.
Controversy over Invention
According to a number of sources, NMR imaging, NMR tomography was first invented in the world in 1960 by V. A. Ivanov [5] [6] . An incompetent expert rejected the application for an invention (method and device) "... because of the obvious futility of the proposed solution," so the copyright certificate was issued for this only more than 10 years later. Thus, it is officially recognized that the author of NMR tomography is not a team of the following Nobel laureates, but a Russian scientist. Despite this legal fact, the Nobel Prize was awarded for MRI tomography not at all to V. A. Ivanov.
Nobel Prizes
The Nobel Prize in Physics for 1952 was awarded to Felix Bloch and Edward Mills Purcell "For the development of new methods for accurate nuclear magnetic measurements and related discoveries."
The 1991 Nobel Prize in Chemistry was awarded to Richard Ernst "For his contribution to the development of high resolution nuclear magnetic resonance spectroscopy methodology".
The Nobel Prize in Chemistry for 2002 (1/2 part) was awarded to Kurt Wutrich “For the development of the application of NMR spectroscopy to determine the three-dimensional structure of biological macromolecules in solution”.
The 2003 Nobel Prize in Physiology and Medicine was awarded to Paul Loterbur and Peter Mansfield “For the invention of the magnetic resonance imaging method”.
Notes
- ↑ Isaac Rabi on Nobelprize.org
- ↑ Purcell EM; Torrey HC; Pound RV Resonance Absorption by Nuclear Magnetic Moments in Solid // Phys. Rev. - 1946. - T. 69 . - pp . 37-38 .
- ↑ Bloch F .; Hansen WW; Packard M. Nuclear Induction // Phys. Rev. - 1946. - T. 69 . - p . 127 .
- ↑ Praxis Dr. B. Sander: MR-Grundlagen
- ↑ T. Bateneva. Interview of V. A. Ivanov with Izvestia, 10.26.2003
- ↑ Ivanov Vladislav Alexandrovich on the website of the Virtual Museum of SPSU ITMO
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