MAGNETIC RESONANCE
resonant (selective) absorption of radio frequency radiation by certain atomic particles placed in a constant magnetic field. Most elementary particles, like tops, rotate around their own axis. If a particle has an electric charge, then when it rotates, a magnetic field arises, i.e. it behaves like a tiny magnet. When this magnet interacts with an external magnetic field, phenomena occur that make it possible to obtain information about nuclei, atoms or molecules, which include this elementary particle. The magnetic resonance method is a universal research tool used in such diverse fields of science as biology, chemistry, geology and physics. There are two main types of magnetic resonances: electron paramagnetic resonance and nuclear magnetic resonance.
See also
MAGNETS AND MAGNETIC PROPERTIES OF SUBSTANCE;
ELEMENTARY PARTICLES.
Electron paramagnetic resonance (EPR). EPR was discovered in 1944 by the Russian physicist E.K. Zavoisky. Electrons in substances behave like microscopic magnets. In different substances, they are reoriented differently if the substance is placed in a constant external magnetic field and exposed to a radio frequency field. The return of electrons to their original orientation is accompanied by a radio frequency signal that carries information about the properties of the electrons and their environment. This method, which is one of the types of spectroscopy, is used in the study of the crystal structure of elements, the chemistry of living cells, chemical bonds in substances, etc.
see also RANGE ; SPECTROSCOPY.
Nuclear magnetic resonance (NMR). NMR was discovered in 1946 by the American physicists E. Purcell and F. Bloch. Working independently of each other, they found a way of resonant "tuning" in magnetic fields of the natural rotations of the nuclei of some atoms, such as hydrogen and one of the isotopes of carbon. When a sample containing such nuclei is placed in a strong magnetic field, their nuclear moments "line up" like iron filings near a permanent magnet. This general orientation can be disturbed by an RF signal. When the signal is turned off, the nuclear moments return to their original state, and the speed of such recovery depends on their energy state, the type of surrounding nuclei, and a number of other factors. The transition is accompanied by the emission of a radio frequency signal. The signal is sent to a computer that processes it. In this way (the method of computed NMR tomography), images can be obtained. (When changing the external magnetic field the effect of a three-dimensional image is achieved in small steps.) The NMR method provides a high contrast of different soft tissues in the image, which is extremely important for identifying diseased cells against the background of healthy ones. NMR tomography is considered safer than X-ray, because it does not cause any destruction or tissue irritation.
(see also X-RAY RADIATION). NMR also makes it possible to study living cells without disturbing their vital activity. Therefore, it should be expected that the use of NMR in clinical medicine will expand. See also SURGERY.
Collier Encyclopedia. - Open Society. 2000 .
See what "MAGNETIC RESONANCE" is in other dictionaries:
elect. absorption by a substance. magn. waves of a certain frequency w, due to a change in the orientation of the magnetic. moments of particles of matter (electrons, at. nuclei). Energy levels of a particle with a magnetic moment m, in ext. magn. field H… … Physical Encyclopedia
elect. absorption in vom el. magn. waves defined. frequency w, due to a change in the orientation of the magnetic. moments h c in va (el new, at. nuclei). Energy levels h tsy, which has a magnet. moment m, in ext. magn. field H is split into magnetic. ... ... Physical Encyclopedia
magnetic resonance- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Engineering, Moscow, 1999] Electrical engineering topics, basic concepts EN magnetic resonance ... Technical Translator's Handbook
Selective absorption by a substance of electromagnetic waves of a certain wavelength, due to a change in the orientation of the magnetic moments of electrons or atomic nuclei. Energy levels of a particle with a magnetic moment (See ... ... Great Soviet Encyclopedia
elect. absorption of email magn. radiation of a certain frequency with a PTO located in the external. magn. field. Due to transitions between magnetic sublevels of the same energy level of the atom, nucleus, and other quantum systems. Naib. important examples of such resonances ... ... Natural science. encyclopedic Dictionary
magnetic resonance- selective absorption by a substance of electromagnetic waves of a certain frequency, due to a change in the orientation of the magnetic moments of the particles of the substance; See also: Resonance nuclear magnetic resonance (NMR) ... Encyclopedic Dictionary of Metallurgy
magnetic resonance- magnetinis rezonansas statusas T sritis chemija apibrėžtis Tam tikro dažnio elektromagnetinių bangų atrankioji sugertis medžiagoje. atitikmenys: engl. magnetic resonance. magnetic resonance... Chemijos terminų aiskinamasis žodynas
- (NMR), selective absorption of email. magn. energy in vom due to nuclear paramagnetism. NMR is one of the methods of radiospectroscopy; it is observed when mutually perpendicular magnetic fields act on the sample under study. fields: strong constant H0 ... Physical Encyclopedia
Image of the human brain on a medical NMR tomograph Nuclear magnetic resonance (NMR) resonant absorption or emission of electromagnetic energy by a substance containing nuclei with non-zero spin in an external magnetic field, at a frequency ν ... ... Wikipedia
- (NAM), selective absorption of acoustic energy. vibrations (phonons), due to the reorientation of the magnetic. moments at. cores in tv. body placed in a permanent magnet. field. For most nuclei, resonant absorption is observed in the ultrasonic region ... ... Physical Encyclopedia
Books
- Magnetic Resonance in Chemistry and Medicine, R. Freeman. The monograph of the well-known scientist in the field of NMR spectroscopy R. Freeman combines the visibility of the consideration of the basic principles of magnetic resonance in chemistry and medicine (biology) with a high…
Nuclear magnetic resonance
VK. Ravens
Irkutsk State Technical University
INTRODUCTION
Until recently, our ideas about the structure of atoms and molecules were based on studies using optical spectroscopy methods. In connection with the improvement spectral methods, which advanced the field of spectroscopic measurements into the range of ultrahigh (approximately 10^ 3 - 10^ 6 MHz; microradio waves) and high frequencies (approximately 10^ (-2) - 10^ 2 MHz; radio waves), new sources of information about the structure of matter have appeared. During the absorption and emission of radiation in this frequency range, the same basic process occurs as in other ranges of the electromagnetic spectrum, namely, when moving from one energy level to another, the system absorbs or emits a quantum of energy.
The energy difference between the levels and the energy of the quanta participating in these processes are about 10^(-7) eV for the radio frequency region and about 10^(-4) eV for microwave frequencies. In two types of radio spectroscopy, namely, nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy, the difference in the energy levels is associated with different orientations, respectively, of the magnetic dipole moments of nuclei in an applied magnetic field and electric quadrupole moments of nuclei in molecular electric fields, if the latter are not spherically symmetrical.
The existence of nuclear moments was first discovered in the study of hyperfine structure electronic spectra some atoms using high resolution optical spectrometers.
Under the influence of an external magnetic field, the magnetic moments of the nuclei are oriented in a certain way, and it becomes possible to observe transitions between nuclear energy levels associated with these different orientations: transitions that occur under the action of radiation of a certain frequency. The quantization of the energy levels of the nucleus is a direct consequence of the quantum nature of the angular momentum of the nucleus receiving 2 I+ 1 values. Spin quantum number(spin) I can be any multiple of 1/2; the highest known value I(> 7) possesses Lu. The largest measurable value of the angular momentum ( highest value projection of the moment on the selected direction) is equal to i ћ , where ћ = h /2 π , a h is Planck's constant.
Values I it is impossible to predict for specific nuclei, but it has been observed that isotopes in which both mass number and atomic number are even have I= 0, and isotopes with odd mass numbers have half-integer spins. Such a situation, when the numbers of protons and neutrons in the nucleus are even and equal ( I= 0) can be considered as a state with “complete pairing”, similar to the complete pairing of electrons in a diamagnetic molecule.
At the end of 1945, two groups of American physicists led by F. Bloch (Stanford University) and E.M. Purcell (Harvard University) were the first to receive nuclear magnetic resonance signals. Bloch observed resonant absorption by protons in water, and Purcell was successful in discovering nuclear resonance by protons in paraffin. For this discovery, they were awarded the Nobel Prize in 1952.
The essence of the NMR phenomenon and its distinctive features are outlined below.
HIGH RESOLUTION NMR SPECTROSCOPY
The essence of the NMR phenomenon
The essence of the NMR phenomenon can be illustrated as follows. If a nucleus with a magnetic moment is placed in a uniform field H 0 , directed along the z axis, then its energy (with respect to the energy in the absence of a field) is equal to μ z H 0, where μ z, is the projection of the nuclear magnetic moment on the direction of the field.
As already noted, the nucleus can be located in 2 I+ 1 states. In the absence of an external field H 0 all these states have the same energy. If we denote the largest measurable value of the magnetic moment component through μ , then all measurable values of the magnetic moment component (in this case μ z,) are expressed as m, where m is the quantum number, which, as is well known, can take the values
m= I, I- 1,I- 2...-(I- 1),-I.
Since the distance between the energy levels corresponding to each of the 2 I+ 1 states, equals m H 0 /I, then the nucleus with spin I has discrete energy levels
- μ H0,-(I-1)μ z H 0 /I,..., (I-1)μ z H 0 /I, μ H0.
The splitting of energy levels in a magnetic field can be called nuclear Zeeman splitting, since it is similar to the splitting of electronic levels in a magnetic field (the Zeeman effect). Zeeman splitting is illustrated in fig. 1 for system with I= 1 (with three energy levels).
Rice. 1. Zeeman splitting of nuclear energy levels in a magnetic field.
The NMR phenomenon consists in the resonant absorption of electromagnetic energy due to the magnetism of the nuclei. This implies the obvious name of the phenomenon: nuclear - we are talking about a system of nuclei, magnetic - we mean only their magnetic properties, resonance - the phenomenon itself is resonant in nature. Indeed, it follows from Bohr's frequency rules that the frequency ν electromagnetic field, which causes transitions between neighboring levels, is determined by the formula
,
(1)
Since the vectors of momentum (angular momentum) and magnetic momentum are parallel, it is often convenient to characterize the magnetic properties of nuclei by the value γ defined by the relation
, (2)
where γ is the gyromagnetic ratio having the dimension radian * oersted^(- 1) * second^(- 1) (rad * E^(- 1) * s*(- 1) ) or radian/(oersted * second) (rad/ (E * s)). With this in mind, we find
, (3)
Thus, the frequency is proportional to the applied field.
If, as a typical example, we take the value of γ for a proton, equal to 2.6753 * 10: 4 rad / (E * s), and H 0 \u003d 10,000 Oe, then the resonant frequency
Such a frequency can be generated by conventional radio techniques.
NMR spectroscopy is characterized by a number of features that distinguish it from other analytical methods. About half (~150) of the nuclei of known isotopes have magnetic moments, but only a minority of them are used systematically.
Before the advent of pulsed spectrometers, most studies were performed using the NMR phenomenon on hydrogen nuclei (protons) 1 H (proton magnetic resonance - PMR) and fluorine 19 F. These nuclei have properties ideal for NMR spectroscopy:
The high natural abundance of the “magnetic” isotope ( 1H 99.98%, 19 F 100%); for comparison, it can be mentioned that the natural abundance of the “magnetic” isotope of carbon 13 C is 1.1%;
Large magnetic moment;
Spin I = 1/2.
This is primarily responsible for the high sensitivity of the method in detecting signals from the nuclei mentioned above. In addition, there is a theoretically rigorously substantiated rule according to which only nuclei with a spin equal to or greater than unity have an electric quadrupole moment. Hence, NMR experiments 1H and 19 F are not complicated by the interaction of the nuclear quadrupole moment of the nucleus with the electric environment. A large number of works have been devoted to resonance at other (besides 1H and 19 F) kernels such as 13 C, 31 P, 11 B, 17 O in the liquid phase (same as on nuclei 1 1H and 19F).
Implementation of NMR pulse spectrometers in daily practice significantly expanded the experimental possibilities of this type of spectroscopy. In particular, the recording of NMR spectra 13 C solutions - the most important isotope for chemistry - is now actually a familiar procedure. The detection of signals from nuclei, the intensity of NMR signals of which is many times less than the intensity of signals from 1 H, including in the solid phase.
High-resolution NMR spectra usually consist of narrow, well-resolved lines (signals) corresponding to magnetic nuclei in various chemical environments. The intensities (areas) of the signals during the recording of the spectra are proportional to the number of magnetic nuclei in each group, which makes it possible to carry out a quantitative analysis using NMR spectra without preliminary calibration.
Another feature of NMR is the influence of exchange processes, in which resonating nuclei participate, on the position and width of resonant signals. Thus, NMR spectra can be used to study the nature of such processes. NMR lines in liquid spectra typically have a width of 0.1 - 1 Hz (high-resolution NMR), while the same nuclei examined in the solid phase will cause the appearance of lines with a width of the order of 1 * 10^ 4 Hz (hence the concept of NMR broad lines).
In high-resolution NMR spectroscopy, there are two main sources of information about the structure and dynamics of molecules:
Chemical shift;
Spin-spin interaction constants.
chemical shift
Under real conditions, resonant nuclei whose NMR signals are detected are integral part atoms or molecules. When the test substances are placed in a magnetic field ( H 0 ) there is a diamagnetic moment of atoms (molecules), due to the orbital motion of electrons. This movement of electrons forms effective currents and, therefore, creates a secondary magnetic field proportional, in accordance with Lenz's law, to the field H 0 and opposite direction. This secondary field acts on the nucleus. Thus, the local field in the place where the resonating nucleus is located,
,
(4)
where σ is a dimensionless constant, called the screening constant and independent of H 0 , but strongly dependent on the chemical (electronic) environment; it characterizes the decrease Hlok compared with H 0 .
Value σ varies from a value of the order of 10^(- 5) for a proton to values of the order of 10^(- 2) for heavy nuclei. Taking into account the expression for Hlok we have
,
(5)
Screening effect is to reduce the distance between the levels of nuclear magnetic energy or, in other words, leads to the convergence of the Zeeman levels (Fig. 2). In this case, the energy quanta that cause transitions between levels become smaller and, consequently, resonance occurs at lower frequencies (see expression (5)). If we conduct an experiment by changing the field H 0 until resonance occurs, the applied field strength must be large compared to the case when the core is not shielded.
Rice. Fig. 2. Effect of electron screening on the Zeeman levels of the nucleus: (a) unscreened, (b) screened.
In the vast majority of NMR spectrometers, spectra are recorded when the field changes from left to right, so the signals (peaks) of the most shielded nuclei should be in the right part of the spectrum.
The shift of the signal depending on the chemical environment, due to the difference in screening constants, is called the chemical shift.
For the first time, messages about the discovery of a chemical shift appeared in several publications in 1950-1951. Among them, it is necessary to single out the work of Arnold et al. (1951), who obtained the first spectrum with separate lines corresponding to chemically different positions of identical nuclei. 1 H in one molecule. It's about about ethyl alcohol CH 3 CH 2 OH, typical NMR spectrum 1 H of which at low resolution is shown in fig. 3.
Rice. 3. Low-resolution proton resonance spectrum of liquid ethyl alcohol.
There are three types of protons in this molecule: three protons of the methyl group CH 3 –, two protons of the methylene group –CH 2 – and one proton of the hydroxyl group –OH. It can be seen that three separate signals correspond to three types of protons. Since the intensity of the signals is in the ratio 3: 2: 1, the decoding of the spectrum (assignment of signals) is not difficult.
Since chemical shifts cannot be measured on an absolute scale, that is, relative to a nucleus devoid of all its electrons, the signal of a reference compound is used as a conditional zero. Usually, the chemical shift values for any nuclei are given as a dimensionless parameter 8 defined as follows:
,
(6)
where H- Hat is the difference in chemical shifts for the test sample and the standard, Hat is the absolute position of the reference signal with the applied field H 0 .
Under real experimental conditions, it is possible to measure the frequency more accurately than the field, so δ is usually found from the expression
,
(7)
where ν - ν floor is the difference between the chemical shifts for the sample and the standard, expressed in units of frequency (Hz); NMR spectra are usually calibrated in these units.
Strictly speaking, one should use ν 0 is the operating frequency of the spectrometer (it is usually fixed), and the frequency ν floor, that is, the absolute frequency at which the resonant signal of the reference is observed. However, the error introduced by such a replacement is very small, since ν 0 and ν floor almost equal (the difference is 10 ^ (-5), that is, by the amount σ for a proton). Since different NMR spectrometers operate at different frequencies ν 0 (and, consequently, for different fields H 0 ), it is obvious that the expression δ in dimensionless units.
The unit of chemical shift is one millionth of the field strength or resonant frequency (ppm). In foreign literature, this reduction corresponds to ppm (parts per million). For most of the nuclei that make up diamagnetic compounds, the range of chemical shifts of their signals is hundreds and thousands of ppm, reaching 20,000 ppm. in case of NMR 59
Co (cobalt). In spectra 1
H proton signals of the vast majority of compounds lie in the range 0 – 10 ppm.
Spin-spin interaction
In 1951-1953, when recording the NMR spectra of a number of liquids, it was found that the spectra of some substances contain more lines than follows from a simple estimate of the number of nonequivalent nuclei. One of the first examples is the resonance on fluorine in the POCl molecule 2 F. Spectrum 19 F consists of two lines of equal intensity, although there is only one fluorine atom in the molecule (Fig. 4). Molecules of other compounds gave symmetrical multiplet signals (triplets, quartets, etc.).
Another important factor found in such spectra was that the distance between the lines, measured in the frequency scale, does not depend on the applied field. H 0 , instead of being proportional to it, as it should be if the multiplicity arises from a difference in screening constants.
Rice. 4. Doublet in the resonance spectrum at fluorine nuclei in the POCl molecule 2F
Ramsey and Purcell in 1952 were the first to explain this interaction by showing that it is due to an indirect coupling mechanism through the electronic environment. The nuclear spin tends to orient the spins of the electrons surrounding the given nucleus. Those, in turn, orient the spins of other electrons and through them - the spins of other nuclei. The spin-spin interaction energy is usually expressed in hertz (that is, the Planck constant is taken as a unit of energy, based on the fact that E=h ν ). It is clear that there is no need (unlike the chemical shift) to express it in relative units, since the discussed interaction, as noted above, does not depend on the strength of the external field. The magnitude of the interaction can be determined by measuring the distance between the components of the corresponding multiplet.
The simplest example of splitting due to spin-spin coupling that can be encountered is the resonance spectrum of a molecule containing two kinds of magnetic nuclei A and X. The nuclei A and X can be either different nuclei or nuclei of the same isotope (for example, 1 H) when the chemical shifts between their resonant signals are large.
Rice. 5. View of the NMR spectrum of a system consisting of magnetic nuclei A and X with spin I = 1/2 when the condition is met δ AX > J AX .
On fig. 5 shows what the NMR spectrum looks like if both nuclei, i.e. A and X, have spin 1/2. The distance between the components in each doublet is called the spin-spin coupling constant and is usually denoted as J (Hz); in this case it is the constant J AH.
The occurrence of doublets is due to the fact that each nucleus splits the resonance lines of the neighboring nucleus into 2I+1 component. The energy differences between different spin states are so small that at thermal equilibrium the probabilities of these states, in accordance with the Boltzmann distribution, turn out to be almost equal. Consequently, the intensities of all lines of the multiplet resulting from interaction with one nucleus will be equal. In the case where there is n equivalent nuclei (that is, equally shielded, so their signals have the same chemical shift), the resonant signal of the neighboring nucleus is split into 2nI + 1 lines.
CONCLUSION
Soon after the discovery of the phenomenon of NMR in condensed matter, it became clear that NMR would be the basis of a powerful method for studying the structure of matter and its properties. Indeed, when studying NMR spectra, we use as a resonant system of nuclei that are extremely sensitive to the magnetic environment. Local magnetic fields near the resonating nucleus depend on intra- and intermolecular effects, which determines the value of this type of spectroscopy for studying the structure and behavior of many-electron (molecular) systems.
At present, it is difficult to point to a field of natural sciences where NMR is not used to some extent. NMR spectroscopy methods are widely used in chemistry, molecular physics, biology, agronomy, medicine, in the study of natural formations (mica, amber, semi-precious stones, combustible minerals and other mineral raw materials), that is, in such scientific areas in which the structure of a substance, its molecular structure, the nature of chemical bonds, intermolecular interactions are studied and various forms internal movement.
NMR methods are increasingly being used to study technological processes in factory laboratories, as well as to control and regulate the course of these processes in various technological communications directly in production. Research over the past fifty years has shown that magnetic resonance methods can detect disturbances in the course of biological processes at the earliest stage. Installations for the study of the entire human body by magnetic resonance methods (NMR tomography methods) have been developed and are being produced.
As for the CIS countries, and above all Russia, magnetic resonance methods (especially NMR) have by now taken a firm place in the research laboratories of these states. In various cities (Moscow, Novosibirsk, Kazan, Tallinn, St. Petersburg, Irkutsk, Rostov-on-Don, etc.), scientific schools arose on the use of these methods with their own original problems and approaches to their solution.
1. Popl J., Schneider W., Bernstein G. High resolution nuclear magnetic resonance spectra. M.: IL, 1962. 292 p.
2. Kerrington A., McLechlan E. Magnetic resonance and its application in chemistry. M.: Mir, 1970. 447 p.
3. Bovi F.A. High resolution NMR of macromolecules. Moscow: Chemistry, 1977. 455 p.
4. Heberlen W., Mehring M. High resolution NMR in solids. M.: Mir, 1980. 504 p.
5. Slikter Ch. Fundamentals of the theory of magnetic resonance. M.: Mir, 1981. 448 p.
6. Ionin B.I., Ershov B.A., Koltsov A.I. NMR spectroscopy in organic chemistry. L.: Chemistry, 1983. 269 p.
7. Voronov V.K. Methods of paramagnetic additives in NMR spectroscopy. Novosibirsk: Nauka, 1989. 168 p.
8. Ernst R., Bodenhausen J., Vokaun A. NMR in one and two dimensions. M.: Mir, 1990. 709 p.
9. Deroum E. Modern NMR methods for chemical research. M.: Mir, 1992. 401 p.
10. Voronov V.K., Sagdeev R.Z. Fundamentals of magnetic resonance. Irkutsk: Vost.-Sib. book. publishing house, 1995.352 p.
The term "magnetic resonance" refers to the selective (resonant) absorption of the energy of an alternating electromagnetic field by an electronic or nuclear subsystem of a substance subjected to a constant magnetic field. The absorption mechanism is associated with quantum transitions in these subsystems between discrete energy levels that occur in the presence of a magnetic field.
Magnetic resonances are usually divided into five types: 1) cyclotron resonance (CR); 2) electron paramagnetic resonance (EPR); 3) nuclear magnetic resonance (NMR); 4) electronic ferromagnetic resonance; 5) electronic antiferromagnetic resonance.
Cyclotron resonance. With CR, selective absorption of electromagnetic field energy is observed in semiconductors and metals in a constant magnetic field, due to quantum transitions of electrons between Landau energy levels. The quasi-continuous energy spectrum of conduction electrons in an external magnetic field is split into such equidistant levels.
The essence of the physical mechanism of CR can also be understood within the framework of the classical theory. A free electron moves in a constant magnetic field (directed along the axis) along a spiral trajectory around magnetic induction lines with a cyclotron frequency
where and are, respectively, the magnitude of the charge and the effective mass of the electron. Let us now turn on the radio frequency field with a frequency and with a vector perpendicular to (for example, along the axis ). If the electron is in the right phase for its helix motion, then since its rotational frequency matches the external field's frequency, it will accelerate and the helix will expand. The acceleration of an electron means an increase in its energy, which occurs due to its transfer from the radio frequency field. Thus, resonant absorption is possible under the following conditions:
the frequency of the external electromagnetic field, the energy of which is absorbed, must coincide with the cyclotron frequency of electrons;
the vector of the electric field strength of the electromagnetic wave must have a component normal to the direction of the constant magnetic field ;
the mean free path of electrons in a crystal must exceed the period of cyclotron oscillations.
The CR method is used to determine the effective mass of carriers in semiconductors. From the half-width of the CR line, one can determine the characteristic scattering times and, thereby, determine the carrier mobility. The area of the line can be used to determine the concentration of charge carriers in the sample.
Electron paramagnetic resonance. The EPR phenomenon consists in the resonant absorption of electromagnetic field energy in paramagnetic samples placed in a constant magnetic field, normal to the magnetic vector of the electromagnetic field. The physical essence of the phenomenon is as follows.
The magnetic moment of an atom with unpaired electrons is determined by expression (5.35). In a magnetic field, the energy levels of an atom, due to the interaction of the magnetic moment with the magnetic field, are split into sublevels with the energy
where is the magnetic quantum number of the atom and takes the value
It can be seen from (5.52) that the number of sublevels is , and the distance between sublevels is
Atomic transitions from low to higher high levels can occur under the influence of an external electromagnetic field. According to the quantum mechanical selection rules, allowed transitions are those in which the magnetic quantum number changes by one, that is, . Therefore, the energy quantum of such a field must be equal to the distance between the sublevels
Relation (5.55) is the EPR condition. An alternating magnetic field of resonant frequency with the same probability will cause transitions from the lower magnetic sublevels to the upper ones (absorption) and vice versa (radiation). In a state of thermodynamic equilibrium, the relationship between the populations and two neighboring levels is determined by the Boltzmann law
It can be seen from (5.56) that states with lower energy have a larger population (). Therefore, the number of atoms absorbing electromagnetic field quanta under these conditions will prevail over the number of emitting atoms; as a result, the system will absorb the energy of the electromagnetic field, which leads to an increase in . However, due to the interaction with the lattice, the absorbed energy in the form of heat is transferred to the lattice, and usually so quickly that, at the frequencies used, the ratio differs very little from its equilibrium value (5.56).
The EPR frequencies can be determined from (5.55). Substituting the value and counting (pure spin moment), we obtain for the resonant frequency
From (5.57) it can be seen that in fields from to 1 T, the resonant frequencies lie in the range of Hz, that is, in the radio frequency and microwave regions.
The resonance condition (5.55) applies to isolated atoms that have magnetic moments. However, it remains valid for a system of atoms, if the interaction between the magnetic moments is negligibly small. Such a system is a paramagnetic crystal, in which magnetic atoms are located at large distances from one another.
The EPR phenomenon was predicted in 1923. Ya.G. Dorfman and experimentally discovered in 1944. E.K.Zavoisky. Currently, EPR is used as one of the most powerful methods for studying solids. Based on the interpretation of EPR spectra, information is obtained on defects, impurities in solids and electronic structure, on the mechanisms chemical reactions etc. Paramagnetic amplifiers and generators have been built on the basis of the EPR phenomenon.
Nuclear magnetic resonance. Heavy elementary particles are protons and neutrons (nucleons), and, consequently, atomic nuclei built from them have their own magnetic moments, which serve as a source of nuclear magnetism. The role of the elementary magnetic moment, by analogy with the electron, is played here by the Bohr nuclear magneton
The atomic nucleus has a magnetic moment
where is the factor of the nucleus, is the spin number of the nucleus, which takes half-integer and integer values:
0, 1/2, 1, 3/2, 2, ... . (5.60)
Projection of the nuclear magnetic moment on the axis z of an arbitrarily chosen coordinate system is determined by the relation
Here, the magnetic quantum number, when known, takes the values:
In the absence of an external magnetic field, all states with different states have the same energy, and therefore are degenerate. An atomic nucleus with a non-zero magnetic moment placed in an external constant magnetic field experiences spatial quantization, and its -fold degenerate level splits into a Zeeman multiplet, the levels of which have energies
If after that the nucleus is affected by an alternating field, the energy quantum of which equal to the distance between levels (5.63)
then there is a resonant absorption of energy by atomic nuclei, which is called nuclear paramagnetic resonance or simply nuclear magnetic resonance.
Due to the fact that is much smaller, the NMR resonant frequency is noticeably lower than the EPR frequency. So NMR in fields of the order of 1 T is observed in the radio frequency region.
NMR as a method for studying nuclei, atoms and molecules has received various applications in physics, chemistry, biology, medicine, technology, in particular, for measuring the strength of magnetic fields.
The traditional method of NMR spectroscopy has many disadvantages. First, it takes a lot of time to build each spectrum. Secondly, it is very picky about the absence of external interference, and, as a rule, the resulting spectra have significant noise. Thirdly, it is unsuitable for creating high-frequency spectrometers. Therefore, in modern NMR instruments, the so-called pulsed spectroscopy method is used, based on the Fourier transform of the received signal.
At present, all NMR spectrometers are built on the basis of powerful superconducting magnets with constant value magnetic field.
The essence of NMR introscopy (or magnetic resonance imaging) is the implementation of a special kind quantitative analysis by the amplitude of the nuclear magnetic resonance signal. In the methods of NMR introscopy, the magnetic field is created by a deliberately inhomogeneous field. Then there is reason to expect that the frequency of nuclear magnetic resonance at each point of the sample has its own value, different from the values in other parts. By specifying some code for NMR signal amplitude gradations (brightness or color on the monitor screen), one can obtain a conditional image (tomogram) of sections of the object's internal structure.
Ferro- and antiferromagnetic resonance. The physical essence of ferromagnetic resonance lies in the fact that under the action of an external magnetic field, magnetizing a ferromagnet to saturation, the total magnetic moment of the sample begins to precess around this field with a Larmor frequency depending on the field. If a high-frequency electromagnetic field perpendicular to is applied to such a sample and its frequency is changed, then at , resonant absorption of the field energy occurs. Absorption in this case is several orders of magnitude higher than in paramagnetic resonance, because the magnetic susceptibility, and, consequently, the magnetic moment of saturation, is much higher in them than in paramagnets.
Features of resonance phenomena in ferro - and antiferromagnets are determined primarily by the fact that in such substances one deals not with isolated atoms or relatively weakly interacting ions of ordinary paramagnetic bodies, but with a complex system of strongly interacting electrons. The exchange (electrostatic) interaction creates a large resulting magnetization, and with it a large internal magnetic field, which significantly changes the resonance conditions (5.55).
Ferromagnetic resonance differs from EPR in that the energy absorption in this case is many orders of magnitude stronger and the resonance condition (relationship between the resonant frequency of the alternating field and the magnitude of the constant magnetic field) depends significantly on the shape of the samples.
Many microwave devices are based on the phenomenon of ferromagnetic resonance: resonant valves and filters, paramagnetic amplifiers, power limiters and delay lines.
Antiferromagnetic resonance ( electronic magnetic resonance in antiferromagnets) - the phenomenon of a relatively large selective response of the magnetic system of an antiferromagnet to the action of an electromagnetic field with a frequency (10-1000 GHz) close to the natural frequencies of the precession of the magnetization vectors of the magnetic sublattices of the system. This phenomenon is accompanied by a strong absorption of the energy of the electromagnetic field.
From a quantum point of view, a antiferromagnetic resonance can be considered as a resonant transformation of electromagnetic field photons into magnons with wave vector .
To observe a antiferromagnetic resonance radio spectrometers are used, similar to those used to study EPR, but allowing measurements at high (up to 1000 GHz) frequencies and in strong (up to 1 MG) magnetic fields. The most promising are spectrometers in which the frequency, rather than the magnetic field, is scanned. Optical methods for detecting a antiferromagnetic resonance.
Nuclear magnetic resonance
nuclear magnetic resonance
Nuclear magnetic resonance (NMR) - resonant absorption of electromagnetic waves by atomic nuclei, which occurs when the orientation of the vectors of their own moments of momentum (spins) changes. NMR occurs in samples placed in a strong constant magnetic field, while simultaneously exposing them to a weak alternating electromagnetic field of the radio frequency range (the lines of force of the alternating field must be perpendicular to lines of force constant field). For hydrogen nuclei (protons) in a constant magnetic field with a strength of 10 4 oersted, resonance occurs at a radio wave frequency of 42.58 MHz. For other nuclei in magnetic fields of 103–104 oersted NMR is observed in the frequency range of 1–10 MHz. NMR is widely used in physics, chemistry and biochemistry to study the structure of solids and complex molecules. In medicine, using NMR with a resolution of 0.5–1 mm, a spatial image of the internal organs of a person is obtained.
Let's consider the phenomenon of NMR on the example of the simplest nucleus - hydrogen. The hydrogen nucleus is a proton, which has a certain value of its own mechanical moment of momentum (spin). In accordance with quantum mechanics, the proton spin vector can have only two mutually opposite directions in space, conventionally denoted by the words “up” and “down”. The proton also has a magnetic moment, the direction of the vector of which is rigidly tied to the direction of the spin vector. Therefore, the vector of the magnetic moment of the proton can be directed either “up” or “down”. Thus, the proton can be represented as a microscopic magnet with two possible orientations in space. If you place a proton in an external constant magnetic field, then the energy of the proton in this field will depend on where its magnetic moment is directed. The energy of a proton will be greater if its magnetic moment (and spin) is directed in the direction opposite to the field. Let's denote this energy as E ↓ . If the magnetic moment (spin) of the proton is directed in the same direction as the field, then the energy of the proton, denoted E, will be less (E<
E ↓).
Пусть протон оказался именно в этом последнем состоянии. Если теперь протону
добавить энергию Δ Е =
E ↓ − E ,
то он сможет скачком перейти в состояние с большей энергией, в котором его
спин будет направлен против поля. Добавить энергию протону можно, “облучая”
его квантами электромагнитных волн с частотой ω, определяемой соотношением
ΔЕ = ћω.
Let's move from a single proton to a macroscopic sample of hydrogen containing a large number of protons. The situation will look like this. In the sample, due to the averaging of random orientations of spins, approximately equal numbers of protons, when a constant external magnetic field is applied, will appear relative to this field with spins directed “up” and “down”. Irradiation of a sample with electromagnetic waves with a frequency ω = (E ↓ − E )/ћ will cause a “massive” spin flip (magnetic moments) of protons, as a result of which all protons of the sample will be in a state with spins directed against the field. Such a massive change in the orientation of protons will be accompanied by a sharp (resonant) absorption of quanta (and energy) of the irradiating electromagnetic field. This is NMR. NMR can only be observed in samples with a large number of nuclei (10 16) using special techniques and highly sensitive instruments.
- The essence of the phenomenon
First of all, it should be noted that although the word “nuclear” is present in the name of this phenomenon, NMR has nothing to do with nuclear physics and has nothing to do with radioactivity. If we talk about a strict description, then one cannot do without the laws of quantum mechanics. According to these laws, the interaction energy of a magnetic core with an external magnetic field can take only a few discrete values. If magnetic nuclei are irradiated with an alternating magnetic field, the frequency of which corresponds to the difference between these discrete energy levels, expressed in frequency units, then the magnetic nuclei begin to move from one level to another, while absorbing the energy of the alternating field. This is the phenomenon of magnetic resonance. This explanation is formally correct, but not very clear. There is another explanation, without quantum mechanics. The magnetic core can be thought of as an electrically charged ball rotating around its axis (although, strictly speaking, this is not the case). According to the laws of electrodynamics, the rotation of a charge leads to the appearance of a magnetic field, i.e., the magnetic moment of the nucleus, which is directed along the axis of rotation. If this magnetic moment is placed in a constant external field, then the vector of this moment begins to precess, i.e., rotate around the direction of the external field. In the same way, the spinning wheel axis precesses (rotates) around the vertical, if it is unwound not strictly vertically, but at a certain angle. In this case, the role of the magnetic field is played by the gravitational force.
The precession frequency is determined both by the properties of the nucleus and by the strength of the magnetic field: the stronger the field, the higher the frequency. Then, if, in addition to a constant external magnetic field, an alternating magnetic field acts on the nucleus, then the nucleus begins to interact with this field - it, as it were, swings the nucleus more strongly, the precession amplitude increases, and the nucleus absorbs the energy of the alternating field. However, this will occur only under the condition of resonance, i.e., the coincidence of the precession frequency and the frequency of the external alternating field. It looks like a classic example from high school physics - soldiers marching across a bridge. If the step frequency coincides with the natural frequency of the bridge, then the bridge sways more and more. Experimentally, this phenomenon manifests itself in the dependence of the absorption of an alternating field on its frequency. At the moment of resonance, the absorption increases sharply, and the simplest magnetic resonance spectrum looks like this:
- Fourier spectroscopy
The first NMR spectrometers worked exactly as described above - the sample was placed in a constant magnetic field, and RF radiation was continuously applied to it. Then either the frequency of the alternating field or the intensity of the constant magnetic field changed smoothly. The energy absorption of the alternating field was recorded by a radio frequency bridge, the signal from which was output to a recorder or an oscilloscope. But this method of signal registration has not been used for a long time. In modern NMR spectrometers, the spectrum is recorded using pulses. The magnetic moments of the nuclei are excited by a short powerful pulse, after which a signal is recorded, which is induced in the RF coil by freely precessing magnetic moments. This signal gradually decreases to zero as the magnetic moments return to equilibrium (this process is called magnetic relaxation). The NMR spectrum is obtained from this signal using a Fourier transform. This is a standard mathematical procedure that allows you to decompose any signal into frequency harmonics and thus obtain the frequency spectrum of this signal. This method of recording the spectrum allows you to significantly reduce the noise level and conduct experiments much faster.
One excitation pulse to record the spectrum is the simplest NMR experiment. However, there can be many such pulses, of different durations, amplitudes, with different delays between them, etc., in the experiment, depending on what kind of manipulations the researcher needs to perform with the system of nuclear magnetic moments. However, almost all of these pulse sequences end in the same thing - recording a free precession signal followed by a Fourier transform.
- Magnetic interactions in matter
In itself, magnetic resonance would remain nothing more than an interesting physical phenomenon, if it were not for the magnetic interactions of nuclei with each other and with the electron shell of the molecule. These interactions affect the resonance parameters, and with their help, the NMR method can be used to obtain a variety of information about the properties of molecules - their orientation, spatial structure (conformation), intermolecular interactions, chemical exchange, rotational and translational dynamics. Thanks to this, NMR has become a very powerful tool for studying substances at the molecular level, which is widely used not only in physics, but mainly in chemistry and molecular biology. An example of one of these interactions is the so-called chemical shift. Its essence is as follows: the electron shell of the molecule responds to an external magnetic field and tries to shield it - partial shielding of the magnetic field occurs in all diamagnetic substances. This means that the magnetic field in the molecule will differ from the external magnetic field by a very small amount, which is called the chemical shift. However, the properties of the electron shell in different parts the molecules are different, and the chemical shift is also different. Accordingly, the resonance conditions for nuclei in different parts of the molecule will also differ. This makes it possible to distinguish chemically nonequivalent nuclei in the spectrum. For example, if we take the spectrum of hydrogen nuclei (protons) of pure water, then there will be only one line in it, since both protons in the H 2 O molecule are exactly the same. But for methyl alcohol CH 3 OH there will already be two lines in the spectrum (if we neglect other magnetic interactions), since there are two types of protons - the protons of the methyl group CH 3 and the proton associated with the oxygen atom. As the molecules become more complex, the number of lines will increase, and if we take such a large and complex molecule as a protein, then in this case the spectrum will look something like this:
- Magnetic cores
NMR can be observed on different nuclei, but it must be said that not all nuclei have a magnetic moment. It often happens that some isotopes have a magnetic moment, while other isotopes of the same nucleus do not. In total, there are more than a hundred isotopes of various chemical elements having magnetic nuclei, however, no more than 1520 magnetic nuclei are usually used in research, everything else is exotic. Each nucleus has its own characteristic ratio of the magnetic field and the precession frequency, called the gyromagnetic ratio. For all nuclei these ratios are known. Using them, one can choose the frequency at which, for a given magnetic field, a signal from the nuclei needed by the researcher will be observed.
The most important nuclei for NMR are protons. They are most abundant in nature, and they have a very high sensitivity. For chemistry and biology, the nuclei of carbon, nitrogen and oxygen are very important, but scientists were not very lucky with them: the most common isotopes of carbon and oxygen, 12 C and 16 O, do not have a magnetic moment, the natural nitrogen isotope 14 N has a moment, but it for a number of reasons it is very inconvenient for experiments. There are 13 C, 15 N and 17 O isotopes that are suitable for NMR experiments, but their natural abundance is very low and the sensitivity is very low compared to protons. Therefore, special isotopically enriched samples are often prepared for NMR studies, in which the natural isotope of one or another nucleus is replaced by the one needed for experiments. In most cases, this procedure is very difficult and expensive, but sometimes it is the only way to get the necessary information.
- Electron paramagnetic and quadrupole resonance
Speaking of NMR, one cannot fail to mention two other related physical phenomena - electron paramagnetic resonance (EPR) and nuclear quadrupole resonance (NQR). EPR is essentially similar to NMR, the difference lies in the fact that the resonance is observed on the magnetic moments not of atomic nuclei, but of the electron shell of the atom. EPR can be observed only in those molecules or chemical groups whose electron shell contains the so-called unpaired electron, then the shell has a non-zero magnetic moment. Such substances are called paramagnets. EPR, like NMR, is also used to study various structural and dynamic properties of substances at the molecular level, but its scope is much narrower. This is mainly due to the fact that most molecules, especially in living nature, do not contain unpaired electrons. In some cases, a so-called paramagnetic probe can be used, i.e. chemical group with an unpaired electron that binds to the molecule under study. But this approach has obvious drawbacks that limit the possibilities of this method. In addition, in EPR there is no such high spectral resolution (ie, the ability to distinguish one line from another in the spectrum) as in NMR.
It is most difficult to explain the nature of NQR "on the fingers". Some nuclei have a so-called electric quadrupole moment. This moment characterizes the deviation of the distribution of the electric charge of the nucleus from spherical symmetry. The interaction of this moment with the gradient of the electric field created by the crystalline structure of the substance leads to the splitting of the energy levels of the nucleus. In this case, resonance can be observed at a frequency corresponding to transitions between these levels. Unlike NMR and EPR, NQR does not require an external magnetic field, since level splitting occurs without it. NQR is also used to study substances, but its scope is even narrower than that of EPR.
- Advantages and disadvantages of NMR
NMR is the most powerful and informative method for studying molecules. Strictly speaking, this is not one method, but a large number of different types of experiments, i.e., pulse sequences. Although they are all based on the NMR phenomenon, but each of these experiments is designed to obtain some specific specific information. The number of these experiments is measured by many tens, if not hundreds. Theoretically, NMR can, if not everything, then almost everything that all other experimental methods for studying the structure and dynamics of molecules can, although in practice this is, of course, far from always feasible. One of the main advantages of NMR is that, on the one hand, its natural probes, i.e., magnetic nuclei, are distributed throughout the molecule, and, on the other hand, it makes it possible to distinguish these nuclei from each other and obtain spatially selective data on properties of the molecule. Almost all other methods provide information either averaged over the entire molecule, or only about one of its parts.
There are two main disadvantages of NMR. First, it is low sensitivity compared to most other experimental methods(optical spectroscopy, fluorescence, EPR, etc.). This leads to the fact that in order to average the noise, the signal must be accumulated for a long time. In some cases, the NMR experiment can be carried out for even several weeks. Secondly, it is its high cost. NMR spectrometers are among the most expensive scientific instruments, costing at least hundreds of thousands of dollars, with the most expensive spectrometers costing several million. Not all laboratories, especially in Russia, can afford to have such scientific equipment.
- Magnets for NMR spectrometers
One of the most important and expensive parts of a spectrometer is the magnet, which creates a constant magnetic field. The stronger the field, the higher the sensitivity and spectral resolution, so scientists and engineers are constantly trying to get the highest possible fields. The magnetic field is created electric shock in a solenoid - the stronger the current, the greater the field. However, it is impossible to increase the current indefinitely; at a very high current, the solenoid wire will simply begin to melt. Therefore, superconducting magnets, i.e., magnets in which the solenoid wire is in the superconducting state, have been used for a very long time for high-field NMR spectrometers. In this case, the electrical resistance of the wire is zero, and no energy is released at any current value. The superconducting state can only be obtained at very low temperatures, just a few degrees Kelvin - this is the temperature of liquid helium. (High-temperature superconductivity is still only a matter of purely fundamental research.) It is with the maintenance of such a low temperature that all the technical difficulties in the design and production of magnets are connected, which cause their high cost. The superconducting magnet is built on the principle of a thermos matryoshka. The solenoid is in the center, in the vacuum chamber. It is surrounded by a shell containing liquid helium. This shell is surrounded by a shell of liquid nitrogen through a vacuum layer. The temperature of liquid nitrogen is minus 196 degrees Celsius, nitrogen is needed so that helium evaporates as slowly as possible. Finally, the nitrogen shell is isolated from room temperature by an outer vacuum layer. Such a system is able to maintain the desired temperature of the superconducting magnet for a very long time, although this requires regular pouring of liquid nitrogen and helium into the magnet. The advantage of such magnets, in addition to the ability to obtain high magnetic fields, is also that they do not consume energy: after the start of the magnet, the current runs through the superconducting wires with virtually no loss for many years.
- Tomography
In conventional NMR spectrometers, they try to make the magnetic field as uniform as possible, this is necessary to improve the spectral resolution. But if the magnetic field inside the sample, on the contrary, is made very inhomogeneous, this opens up fundamentally new possibilities for using NMR. The inhomogeneity of the field is created by the so-called gradient coils, which are paired with the main magnet. In this case, the magnitude of the magnetic field in different parts of the sample will be different, which means that the NMR signal can be observed not from the entire sample, as in a conventional spectrometer, but only from its narrow layer, for which resonance conditions are met, i.e., the desired ratio of magnetic field and frequency. By changing the magnitude of the magnetic field (or, which is essentially the same thing, the frequency of observing the signal), you can change the layer that will give the signal. Thus, it is possible to "scan" the sample throughout its volume and "see" its internal three-dimensional structure without destroying the sample in any mechanical way. To date, a large number of techniques have been developed that make it possible to measure various NMR parameters (spectral characteristics, magnetic relaxation times, self-diffusion rate, and some others) with spatial resolution inside a sample. The most interesting and important, from a practical point of view, the use of NMR tomography was found in medicine. In this case, the "sample" being examined is the human body. NMR imaging is one of the most effective and safe (but also expensive) diagnostic tools in various fields of medicine, from oncology to obstetrics. It is curious to note that doctors do not use the word "nuclear" in the name of this method, because some patients associate it with nuclear reactions and the atomic bomb.
- Discovery history
The year of the discovery of NMR is considered to be 1945, when the Americans Felix Bloch from Stanford and independently Edward Parcell and Robert Pound from Harvard first observed the NMR signal on protons. By that time, much was already known about the nature of nuclear magnetism, the NMR effect itself was theoretically predicted, and several attempts were made to observe it experimentally. It is important to note that a year earlier in the Soviet Union, in Kazan, the EPR phenomenon was discovered by Evgeny Zavoisky. It is now well known that Zavoisky also observed the NMR signal, this was before the war, in 1941. However, he had a poor quality magnet with poor field uniformity at his disposal, the results were poorly reproducible and therefore remained unpublished. In fairness, it should be noted that Zavoisky was not the only one who observed NMR before its "official" discovery. In particular, the American physicist Isidore Rabi (Nobel Prize winner in 1944 for the study of the magnetic properties of nuclei in atomic and molecular beams) also observed NMR in the late 1930s, but considered this to be an instrumental artifact. One way or another, but our country remains a priority in the experimental detection of magnetic resonance. Although Zavoisky himself soon after the war began to deal with other problems, his discovery for the development of science in Kazan played a huge role. Kazan is still one of the world's leading research centers for EPR spectroscopy.
- Nobel Prizes in Magnetic Resonance
In the first half of the 20th century, several Nobel Prizes were awarded to scientists without whose work the discovery of NMR could not have taken place. Among them are Peter Szeeman, Otto Stern, Isidor Rabi, Wolfgang Pauli. But there were four Nobel Prizes directly related to NMR. In 1952, Felix Bloch and Edward Purcell received the prize for the discovery of NMR. This is the only "NMR" Nobel Prize in physics. In 1991, the Swiss Richard Ernst, who worked at the famous ETH Zurich, won the Chemistry Prize. He was awarded it for the development of multidimensional NMR spectroscopy methods, which made it possible to radically increase the information content of NMR experiments. In 2002, the prize winner, also in chemistry, was Kurt Wüthrich, who worked with Ernst in neighboring buildings at the same Technical School. He received the award for developing methods for determining the three-dimensional structure of proteins in solution. Prior to this, the only method that allowed determining the spatial conformation of large biomacromolecules was only X-ray diffraction analysis. Finally, in 2003, the American Paul Lauterbur and the Englishman Peter Mansfield received the Medical Prize for the invention of NMR imaging. The Soviet discoverer of the EPR E.K. Zavoisky, alas, did not receive the Nobel Prize.