EPR is observed in solids (crystalline, polycrystalline and powdery), as well as liquid and gaseous. The most important condition for observing EPR is the absence of electrical conductivity and macroscopic magnetization in the sample.
Under favorable conditions, the minimum number of spins that can be recorded in the test sample is 1010. The sample weight can be, in this case, from a few micrograms to 500 milligrams. During the EPR study, the sample is not destroyed and can be used later for other experiments.
Electronic paramagnetic resonance
The phenomenon of electron paramagnetic resonance (EPR) consists in the resonant absorption of electromagnetic radiation in the radio frequency range by substances placed in a constant magnetic field, and is caused by quantum transitions between energy sublevels associated with the presence of a magnetic moment in electronic systems. Also called EPR electron spin resonance (ESR), magnetic spin resonance (MSR) and, among specialists working with magnetically ordered systems, ferromagnetic resonance (FMR).
The EPR phenomenon can be observed on:
- atoms and molecules that have an odd number of electrons in their orbitals - H, N, NO 2, etc .;
- chemical elements in various charge states, in which not all electrons in the outer orbitals participate in the formation of a chemical bond - first of all, these are d- and f-elements;
- free radicals - methyl radical, nitroxyl radicals, etc .;
- electronic and hole defects stabilized in the matrix of substances - O -, O 2 -, CO 2 -, CO 2 3-, CO 3 -, CO 3 3- and many others;
- molecules with an even number of electrons, the paramagnetism of which is due to the quantum phenomena of the distribution of electrons over molecular orbitals - О 2;
- superparamagnetic nanoparticles formed during dissolution or in alloys with a collective magnetic moment, which behave like an electron gas.
The structure and properties of the EPR spectra
The behavior of magnetic moments in a magnetic field depends on various interactions of unpaired electrons, both among themselves and with the nearest environment. The most important of them are spin-spin and spin-orbit interactions, interactions between unpaired electrons and nuclei on which they are localized (hyperfine interactions), interactions with the electrostatic potential created by ions of the nearest environment at the site of localization of unpaired electrons, and others. Most of the listed interactions lead to a regular line splitting. In general, the EPR spectrum of a paramagnetic center is multicomponent. An idea of \u200b\u200bthe hierarchy of basic splits can be obtained from the following diagram (definitions of the used notation are given below):
The main characteristics of the EPR spectrum of a paramagnetic center (PC) are:
the number of lines in the EPR spectrum of a particular PC and their relative intensities.
Fine structure (TS). The number of TS lines is determined by the magnitude of the spin S of the PC and the local symmetry of the electrostatic field of the nearest environment, and the relative integral intensities are determined by the quantum number mS (the magnitude of the spin projection on the direction of the magnetic field). In crystals, the distance between the TS lines depends on the magnitude of the potential of the crystal field and its symmetry.
Ultrafine structure (STS). The HFS lines from a particular isotope have approximately the same integral intensity and are practically equidistant. If the core of a QC has several isotopes, then each isotope gives its own set of HFS lines. Their number is determined by the spin I of the isotope nucleus, around which the unpaired electron is localized. The relative intensities of the HFS lines from various isotopes of the PC are proportional to the natural abundance of these isotopes in the sample, and the distance between the HFS lines depends on the magnetic moment of the nucleus of a particular isotope, the hyperfine interaction constant, and the degree of delocalization of unpaired electrons on this nucleus.
Superhyperfine structure (SSFS). The number of SHFS lines depends on the number nl of equivalent ligands with which the unpaired spin density interacts and the value of the nuclear spin Il of their isotopes. A characteristic feature of such lines is also the distribution of their integral intensities, which in the case of I l \u003d 1/2 obeys the law of binomial distribution with the exponent n l. The distance between the SHFS lines depends on the magnitude of the magnetic moment of the nuclei, the hyperfine interaction constant, and the degree of localization of unpaired electrons on these nuclei.
spectroscopic characteristics of the line.
A feature of the EPR spectra is the form of their recording. For many reasons, the EPR spectrum is not recorded as absorption lines, but as a derivative of these lines. Therefore, in EPR spectroscopy, a slightly different, different from the generally accepted, terminology for designating the parameters of lines is adopted.
EPR absorption line and its first derivative: 1 - Gaussian shape; 2 - Lorentzian form.
The true line is the δ-function, but taking into account relaxation processes it has the Lorentz shape.
Line - reflects the probability of the process of resonant absorption of electromagnetic radiation by the PC and is determined by the processes in which the spins participate.
Line shape - reflects the law of the distribution of the probability of resonant transitions. Since, to a first approximation, deviations from the resonance conditions are random, the shape of the lines in magnetically diluted matrices has a Gaussian shape. The presence of additional exchange spin-spin interactions leads to the Lorentzian shape of the line. In general, the line shape is described by a mixed law.
Line width - ΔВ max - corresponds to the distance across the field between the extrema on the curved line.
The amplitude of the line - I max - corresponds on the scale of the signal amplitude to the distance between the extrema on the curve of the line.
Intensity - I 0 - the value of the probability at the MAX point on the absorption curve, calculated by integration along the contour of the recording line;
Integral intensity - the area under the absorption curve, is proportional to the number of paramagnetic centers in the sample and is calculated by double integration of the recording line, first along the contour, then along the field.
The position of the line - B 0 - corresponds to the intersection of the contour of the dI / dB derivative with the zero line (trend line).
the position of the EPR lines in the spectrum.
According to the expression ħν \u003d gβB, which determines the conditions of resonance absorption for a QC with spin S \u003d 1/2, the position of the electron paramagnetic resonance line can be characterized by the value of the g factor (an analogue of the Lande spectroscopic splitting factor). The value of the g-factor is defined as the ratio of the frequency ν at which the spectrum was measured to the value of the magnetic induction B 0 at which the maximum effect was observed. It should be noted that for paramagnetic centers the g-factor characterizes the PC as a whole, i.e., not a separate line in the EPR spectrum, but the entire set of lines caused by the PC under study.
In EPR experiments, the energy of an electromagnetic quantum is fixed, that is, the frequency ν, and the magnetic field B can vary over a wide range. There are some rather narrow microwave frequency ranges in which spectrometers operate. Each range has its own designation:
| Range (BAND) |
Frequency ν, MHz (GHz) |
Wavelength λ, mm |
Magnetic induction B0, at which the EPR signal of a free electron is observed with g \u003d 2.0023, G (T) |
|---|---|---|---|
The most widely used spectrometers are X- and Q-ranges. The magnetic field in such EPR spectrometers is created by resistive electromagnets. In spectrometers with a higher quantum energy, the magnetic field is created on the basis of superconducting magnets. At present, the EPR equipment at RC MRMI is a multifunctional X-band spectrometer with a resistive magnet, which allows experiments in magnetic fields with an induction from -11000 G to 11000 G.
The basic one is the CW mode or the mode of slow differential passage through resonant conditions. In this mode, all classical spectroscopic techniques are implemented. It is intended to obtain information about the physical nature of the paramagnetic center, the place of its localization in the matrix of the substance and its nearest atomic-molecular environment. Investigations of the QC in the CW mode allow obtaining, first of all, comprehensive information about the possible energy states of the object under study. Information on the dynamic characteristics of spin systems can be obtained by observing the EPR, for example, at different temperatures of the sample or upon exposure to photons. For PCs in a triplet state, additional photoirradiation of the sample is mandatory.
Example
The figure shows the spectrum of the enamel of a bison tooth (lat. Bison antiquus) from a collection selected in 2005 by the Siberian archaeological expedition of the IIMK RAS, which carried out rescue excavations at the Upper Paleolithic site Berezovsky cut 2 located on the territory of the Berezovsky 1 coal mine.
Tooth enamel consists of almost pure hydroxyapatite Ca (1) 4 Ca (2) 6 (PO 4) 6 (OH) 2. The structure of hydroxyapatite also contains 3-4% carbonates.
Irradiation of crushed tooth enamel with gamma radiation leads to the emergence of a complex asymmetric signal (AS) of the EPR near the value g \u003d 2. This signal is studied in the problems of dosimetry, dating, medicine, and as a source of information on the structure of apatite.
The main part of the radicals arising from irradiation of tooth enamel are carbonate anions, i.e. CO 2 -, CO 3 -, CO - and CO 3 3-.
The spectrum recorded a signal from axially symmetric paramagnetic centers CO 2 - with g ‖ \u003d 1.9975 ± 0.0005 and g \u003d 2.0032 ± 0.0005. The signal is radio-induced, that is, PCs were formed under the action of ionizing radiation (radiation).
The intensity of the CO 2 signal - carries information about the radiation dose received by the object during its existence. In particular, dosimetric methods of analysis and control of radiation (GOST R 22.3.04-96) are based on studies of CO 2 signals in the spectra of tooth enamel. In this and many other cases, dating of a mineral sample by EPR is possible. The age range covered by EPR dating is from hundreds of years to 105 and even 106 years, which exceeds the capabilities of the radiocarbon method. The sample, the spectra of which are shown in the figure, was dated by the EPR method and is 18000 ± 3000 years old.
To study the dynamic characteristics of centers, it is advisable to use pulse methods. In this case, the FT-mode of the EPR spectrometer is used. In such experiments, a sample in a certain energy state is subjected to a strong pulsed effect of electromagnetic radiation. The spin system is unbalanced, and the system's response to this action is recorded. By choosing different sequences of pulses and varying their parameters (pulse duration, distance between pulses, amplitude, etc.), one can significantly expand the understanding of the dynamic characteristics of the PC (relaxation times T 1 and T 2, diffusion, etc.).
3. ESE (electron spin echo technique)
The ESE method can be used to obtain a double electron-nuclear resonance spectrum to save recording time or in the absence of dedicated ENDOR equipment.
Example:
Test sample: tooth enamel consisting of hydroxyapatite Ca (1) 4 Ca (2) 6 (PO 4) 6 (OH) 2. The signal of CO 2 - radicals in the structure of hydroxyapatite was studied.
Free induction decay (FID) is represented by a set of oscillations called modulation. Modulation carries information about the resonance frequencies of the nuclei surrounding the paramagnetic center. As a result of the Fourier transform of the FID time dependence, the spectrum of nuclear magnetic resonance was obtained. At a frequency of 14 MHz, there is a 1H signal, therefore, the studied CO 2 groups - interact with the protons located in their environment.
4. ENDOR
The most widespread technique of double resonance is the method of double electron-nuclear resonance - ENDOR, which makes it possible to study the processes of interaction of an unpaired electron both with its own nucleus and with the nuclei of its immediate environment. In this case, the sensitivity of the NMR method can increase by tens and even thousands of times in relation to standard methods. The described techniques are implemented in both CW and FT modes.
Example
The figure shows the ENDOR spectrum of biological hydroxyapatite (tooth enamel). The method was used to obtain information about the environment of the paramagnetic centers CO 2 - contained in the enamel. Signals from the nuclear environment of the CO 2 center were recorded - at 14 MHz and 5.6 MHz. The signal at 14 MHz refers to hydrogen nuclei, and the signal at 5.6 MHz refers to phosphorus nuclei. Based on the structural features of biological apatite, it can be concluded that the investigated paramagnetic center CO 2 - is surrounded by OH - and PO 4 - anions.
5. ELDOR (currently not available in the RC)
ELDOR (ELectron DOuble Resonance) is a kind of double resonance technique. In this method, the interaction between two electron spin systems is studied, and the EPR spectrum from one electronic system is recorded by excitation of the other. To observe a signal, there must be a mechanism connecting the "observed" and "pumped" systems. Examples of such mechanisms are dipole interaction between spins, molecular motion.
ELECTRONIC PARAMAGNETIC RESONANCE (EPR) - resonant absorption (radiation) of the electromagnet. waves of the radio frequency range (10 9 -10 12 Hz) by paramagnets, the paramagnetism of which is due to electrons. EPR is a special case of paramagnet. resonance and more general phenomenon - magnetic resonance... Underlies radio spectroscopic. methods for studying a substance (see. Radiospectroscopy)... It has a synonym - electron spin resonance (ESR), which emphasizes the important role in the phenomenon of electron spins. Discovered in 1944 by E.K. Zavoisky (USSR). As a paramagnet. particles (in the case of condensed media, paramagnetic centers), which determine paramagnetism, can be electrons, atoms, molecules, complex compounds, crystal defects, if they have a nonzero magnetic moment... The source of the occurrence of magn. moment can be unpaired spin or nonzero total spin (moment of number of motion) of electrons.
In permanent magn. fields as a result of lifting the degeneracy of the paramagnets. particles there is a system of magn. (spin) sublevels (see. Zeeman effect). Between them, under the influence of an electromagnet. radiation, transitions arise that lead to the absorption (emission) of a photon with a frequency w ij \u003d | | /. In the case of one electron in a permanent magn. field H
energy of sublevels \u003d bgb H /2 and, accordingly, the EPR frequency w is determined by the relation
where g is the spectroscopic factor. splitting; b - Bohr magneton; usually, H\u003d 10 3 5-10 4 Oe; g2.
Experimental Methods... EPR spectrometers (radio spectrometers) operate in the centimeter and millimeter wavelength ranges. The technique of the microwave range is used - a generator (usually klystron), a system of waveguides and resonators with a detecting device. A sample with a volume of several. mm 3 is placed in the region of the resonator, where the component of the electromagnet. waves (usually magnetic) that cause transitions have an antinode. The resonator is installed between the poles of an electromagnet - a permanent magnet source. fields. A resonant condition like (1) is usually achieved by varying the field strength H at a fixed value of the generator frequency w. The value of the magn. field at resonance ( H p) generally depends on the orientation of the vector H
in relation to the sample. An absorption signal in the form of a typical bell-shaped burst or its derivative (Fig. 1) is observed with an oscilloscope or a recorder. Naib. often investigated the absorption signal proportional to the imaginary part of the dynamic magn. susceptibility (c "") of the sample. However, in a number of cases, its real part (c ") is recorded, which determines the fraction of magnetization that changes in phase with the magnetic component of the electromagnetic wave. EPR can manifest itself in the form of microwave analogs of the optical Faraday and Cotton-Mouton effects. waveguides, at the end of which special antennas are installed, rotating around the axis of the waveguide and measuring the rotation of the plane of polarization or the ellipticity of the wave emerging from the sample.Pulse methods are widely used to analyze the time dependences of EPR signals (the so-called spin induction and spin echoThere are also a number of other techniques for studying relaxation. processes, in particular for measuring relaxation times.
Figure: 1. Electronic paramagnetic resonance: and
- spin paramagnetic particle S \u003d 1/2, placednaya in an external magnetic field, has two sublevels ( and), each of which changes proportionrationally to the field H and depends on its orientation along relation to the crystallographic axes,my angles are q and f. At resonance values, the magnetfoot field H p1 and H р2 (angles q 1, (j 1 and q 2, j 2) the difference becomes equal to the microwave energy quantum-radiation. In this case, in the absorption spectrum ( b) observecharacteristic bursts are given near N p 1 and H p 2 (atabsorption signal and its derivative are entered).
Theoretical description... To describe the EPR spectrum, we use spin Hamiltonian , to-ry for each specific case has its own form. In the general case, it can be presented in a form that takes into account all possible interactions of paramagnets. particles (center):
where describes interaction with ext. magn. field H
;
- interaction with intracrystalline. electric field; - with magn. the moment of its own and surrounding nuclei ( hyperfine interaction and superhyperfine interaction); - spin-spin interactions paramagnet. centers among themselves (exchange interaction, dipole-dipole, etc.); -interaction with the attached ext. pressure P (deformations); -with external electric field E
... Each term included in (2) may consist of several. terms, the form of which depends on the magnitude of the electronic and nuclear spins and the local symmetry of the center. Frequently used expressions are of the form;
where g, a, A, J, C, R-theory parameters, S
(i) and I
(k)
- ith and kth spin of electrons and nucleus; - identity matrix. The spin Hamiltonian (2) is usually referred to one electronic or electron-oscillation. term (usually the main one), assuming that the other terms are spaced from it by an amount significantly exceeding the quantum energy of the EPR transition. But in some cases, for example. in the presence of Jan-Teller effect, the excited terms can be close enough and they must be taken into account when describing the EPR spectra. Then, to preserve the formalism of the spin Hamiltonian, we can introduce eff. spin ( S eff), associated with the total number of states of all levels ( r) by the relation r = 2S eff +1. Another approach is possible within the framework of the perturbation matrix method: the complete matrix of the perturbation operator is found at all states of the levels taken into account.
Each of the terms (2) can be divided into two parts: static and dynamic. Static. the part determines the position of the lines in the spectrum, the dynamic part determines the probabilities of quantum transitions, including those determining and relaxation. processes. Energetic. the structure and wave functions are found by solving the system of equations corresponding to (2). The number of ur-ny is
where n and pis the number of spins of electrons and nuclei appearing in (2). Usually S and I take values \u200b\u200bfrom 1/2 to 7/2 ; n \u003d1,
2; p \u003d l-50, which indicates the possibility of the existence of high-order secular ur-nes. To overcome the tech. difficulties in diagonalization (2), approximate (analytical) calculations are used. Not all terms (2) are the same in magnitude. Usually they are superior to other members, and much less than the previous ones. This allows us to develop the theory of perturbations in several. stages. In addition, specials have been developed. computer programs.
The goal is phenomenological. theory - finding for def. transition expression for H p in the f-tion of the parameters of the spin Hamiltonian and the angles characterizing the orientation of the ext. fields relatively crystallographic. axes. By matching ( H p) theor with ( H p) exp, the correctness of the choice of (2) is established and the parameters of the spin Hamiltonian are found.
The parameters of the spin Hamiltonian are calculated independently using the methods of quantum mechanics, based on the definition. paramagnet models. center. This uses the theory of crystalline. fields, molecular orbital method, other methods quantum chemistry and solid state theory. Main the difficulty of this problem lies in the definition of electronic energetic. structures and wave f-tions of paramagnets. centers. If these components of the Schrödinger equation are found, and the perturbation operators are known, the problem is reduced to calculating only the corresponding matrix elements. Due to the complexity of the whole complex of problems, there have been little complete calculations of the parameters of the spin Hamiltonian, and not all of them have achieved satisfactory agreement with experiment. Usually they are limited to estimates in order of magnitude using approximate f-ly.
The EPR spectrum (the number of lines, their dependence on the orientation of external fields relative to the crystallographic axes) is completely determined by the spin Hamiltonian. So, in the presence of only the Zeeman interaction, the expression for the energy has the form \u003d gb H +
Mwhere M is the quantum number of the operator taking 2 S+1 values: - S, - S +1, .... S-1, S. Magn. component e - magn. waves in this case cause only transitions with the selection rules DM \u003d b 1, and, due to the equidistance of the levels, one line will be observed in the EPR spectrum. The violation of equidistance arises due to other terms of the spin Hamiltonian. Thus, an axially symmetric term from, characterized by the parameter D, adds to the term 
,
H p turns out to depend on M, and the spectrum will observe 2 S lines. Taking into account the term AS z I z from leads to the addition (D
) st \u003d AMtwhere t is the quantum number of the operator I z; H p will depend on m, and in the EPR spectrum there will be 2 I + 1 line. Other terms from (2) can lead to additional, "forbidden" selection rules (for example, D M\u003d b2), which increases the number of lines in the spectrum.
Specific splitting of lines occurs under the action of electric. fields (term). In crystals (corundum, wolframite, silicon) there are often inversion nonequivalent positions, in which impurity ions can be found with equal probability. Since the magn. the field is insensitive to the inversion operation, it does not distinguish between these positions, and in the EPR spectrum the lines from them coincide. Electricity applied to the crystal the field for different nonequivalent positions due to their mutual inversion will be directed in opposite directions. Amendments to H p (linear in E) from different positions will have opposite signs, and the mixing of the two groups of lines will manifest itself in the form of splitting.
In the absence of magn. field (\u003d 0), the splitting of levels, called the initial splitting, is due to other terms (2). The number of emerging levels and the multiplicity of their degeneracy depend on the magnitude of the spin and the symmetry of the paramagnets. center. Transitions between them are possible (the corresponding phenomenon was called un-field-of-field-resonance). For its implementation, you can change the frequency v of the electromagnet. radiation, or at v \u003d const change the distance between the levels ext. electric field, pressure, temperature change.
Determination of the symmetry of the paramagnetic center... Angle dependence H p (q, f) reflects the symmetry of the spin Hamiltonian, which, in turn, is associated with the symmetry of the paramagnet. center. This makes it possible by the type of function H p (q, f) found experimentally to determine the symmetry of the center. In the case of highly symmetric groups ( About h, T d, C 4u, etc.) function H p (q, f) has a number of characteristic features: 1) the positions of the extrema for the lines of different transitions coincide; 2) the distance between the extrema is p / 2 (orthogonality effect); 3) f-tion H p is symmetric with respect to the positions of extrema, etc. In the case of low-symmetry groups ( C 1 ,
C 2 , C 3, etc.), all these patterns are violated (effects of low symmetry). These effects are used to determine the structure of defects.
The usual EPR corresponds to the spin Hamiltonian, which does not take into account electric. fields (\u003d 0). It includes only operators of the moment of the number of movements and magn. fields. Due to their pseudo-vector nature, max. the number of mismatched spin Hamiltonians will be 11 (out of 32 possible point groups). This leads to ambiguity in determining the symmetry of paramagnets. centers, to-ruyu can be eliminated using ext. electric field. Linear by E
the operator is different for different point groups that do not have an inversion center (for inversion centers \u003d 0). At the 1st stage from experiments without a field E the set of groups with the same Hamiltonian is defined, which corresponds to the symmetry of the spectrum of the usual EPR. At the 2nd stage, the field is used E
and the fact is taken into account that each set of groups includes only one group with an inversion center.
Investigation of disordered systems... Along with the study of paramagnets. centers in perfect crystals EPR is also used to study disordered systems (powders, glasses, solutions, crystals with defects). A feature of such systems is the unevenness (heterogeneity) of conditions at the locations of the centers due to differences in the internal. electric (magn.) fields and deformations caused by structural distortions of the crystal; nonequivalence of orientation of paramagnets. centers in relation to the outside. fields; heterogeneity of the latter. This leads to a scatter in the parameters of the spin Hamiltonian and, as a consequence, to inhomogeneous broadening of the EPR lines. The study of these lines provides information on the nature and degree of crystal defects. An inhomogeneous broadening of any nature can be considered from a unified point of view. The general expression for the line shape is:
where y is a function that describes the original line shape without taking into account disturbing factors; V
(F) - the probability of transition per unit of time; r ( F) - f-tion of the distribution of parameters F (F 1 , F 2 , . ·., F k)that characterize the broadening mechanisms (components of fields, deformations, angles). So, in the case of chaotically oriented paramagnets. centers (powders) under F should be understood as the Euler angles characterizing the orientation of the powder particle with respect to the coordinate system associated with the external. fields. In fig. 2 shows a typical EPR spectrum of a powder for a spin Hamiltonian of the form 
Instead of ang. dependence of a single narrow line inherent in paramagnets. centers in single crystals, in this case an orientationally broadened envelope line appears.
Figure: 2. Signal of electron paramagnetic resonanceca chaotically oriented paramagnetic centers. Absorption line ( and) and its derivative ( b
) in the case of rhombic symmetry of the spin Hamiltoniana. The characteristic points of the spectrum are related to the parameters of the spin Hamiltonian by the relation H pi\u003d w / bg iii
.
Relaxation processes... EPR is accompanied by the processes of restoration of the damaged electromagnet. radiation of equilibrium in the medium corresponding to the Boltzmann distribution. These relaxers. processes are due to the connection between paramagnets. center and grid, as well as centers between gather. Accordingly, they are distinguished with p and n-e w e-current and with p and n-s p and y relaxation. If the transitions are under the influence of electromagnet. waves predominate, saturation occurs (leveling of the level populations), which manifests itself in a decrease in the EPR signal. Relaxation. processes are characterized by relaxation times and are described by kinetic. ur-niy (see. The kinetic equation is basic)... In case of two levels i and j ur-niya for populations n i and n j- have the form
where a \u003du 0 ij + u ij, b \u003du 0 ji + u ji, u 0 ij and u ij-probabilities of transition per unit of time from the level i to the level j under the influence of e - magn. waves and relaxation. mechanisms respectively (
u 0 ij \u003d u 0 ji)... Relaxation time T p is determined by the expression T p \u003d (u ij+ u ji) -1 and characterizes the rate of equilibrium establishment. Relaxation. the processes, determining the lifetimes of particles at spin levels, lead to their broadening, which affects the width and shape of the EPR line. This broadening, a cut in the same way manifests itself in all paramagnets. centers are usually called homogeneous. It defines, in particular, the function y included in (3).
Double resonances... To describe the spin system, the concept of the pin temperature was introduced T s... The defining Boltzmann distribution, the relationship between the level population and temperature is generalized to the case of non-equilibrium populations. From it, with arbitrary ratios of populations, top. ( n in) and lower. ( n m) levels it follows that Т s \u003d - () / ln ( n in / n n). When n in \u003d n n (saturation) T s \u003dand at n in\u003e n n value T s<
0. The possibility of creating a non-equilibrium population and, in particular, situations in which T s \u003d and T s<0, привело к развитию двойных резонансов на базе
ЭПР. Они характеризуются тем, что при наличии многоуровневой системы осуществляются
резонансные переходы одновременно (или в опре-дел. последовательности) на двух
частотах (рис. 3). Цель осуществления двойных резонансов: увеличение интенсивности
поглощения за счёт увеличения разности населённостей (рис. 3, and); obtaining a source of e - magn. radiation by creating a larger population at the upper level than at the lower (Fig. 3, b)... The principle of signal amplification formed the basis for the realization of a number of double resonances in cases when the system contains spins of different types. So, in the presence of electronic and nuclear spins, a double electronic nuclear resonance (ENER) is possible. The hyperfine level splitting is usually much less than the Zeeman one. This makes it possible to enhance transitions between hyperfine sublevels by saturating spin-electron transitions. The ENDOR method increases not only the sensitivity of the apparatus, but also its resolution, since hyperfine interactions with each nucleus can be observed directly in the corresponding spin-nuclear transition (while the analysis of the hyperfine structure from the EPR spectrum is in many cases for overlapping lines). Due to these advantages, ENDOR has found wide application in solid state physics, and in particular in semiconductor physics. With its help, it is possible to analyze the nuclei of many coordinates. spheres near the defect, which makes it possible to unambiguously determine its nature and properties. Double resonances associated with obtaining sources of electromagnet. radiation, formed the basis of the work of quantum generators, which led to the creation and development of a new direction - quantum electronics.
Figure: 3. Double resonance in a multilevel system. There are 3 levels, for which and n 1 0 - n 0 2 \u003e\u003e n 0 2 - P 0 3 (p 0 - equilibrium value); and - gain absorption; intense electromagnetic radiation saturates levels 1 and 2, so that n 1 n 2
= (n 0 1 +
n 0 2) / 2; as a result p 2 - p 3 increases by ( n 0 1 - n 0 2 )/
2, and the absorption signal at the frequency v 32 rises sharply;
b-maser effect; saturation of levels 1 and 3dit to the necessary condition [ n 3 -n 2 (n 0 1 -n 0 2) / 2\u003e 0] for generating e - magn. radiation at frequency v 32
Conclusion... EPR has found wide application in decomp. areas of physics, chemistry, geology, biology, medicine. It is intensively used to study the surface of solids, phase transitions, disordered systems. In semiconductor physics, EPR is used to study shallow and deep point impurity centers, free charge carriers, carrier-impurity pairs and complexes, and radiation. defects, dislocations, structural defects, amorphization defects, interlayer formations (such as Si - SiO 2 boundaries), the carrier-impurity interaction, recombination processes, photoconductivity and other phenomena are being studied.
Lit .: Altshuler S.A., Kozyrev B.M., Electron paramagnetic resonance of compounds of elements of intermediate groups, 2 ed., M., 1972; Poole Ch., Technique of EPR spectroscopy, trans. from English, M., 1970; Abraham A., Blini B., Electron paramagnetic resonance of transition ions, trans. from English, G. 1-2, M., 1972-73; Meilman ML, Samoilovich MI, Introduction to EPR spectroscopy of activated single crystals, M., 1977; Electrical Effects in Radiospectroscopy, ed. M. F. Dey-gena, M., 1981; Roytsin AB, Maevsky V. H., Radiospectroscopy of the surface of solids, K., 1992; Solid State Radiospectroscopy, ed. A. B. Roytsina, K., 1992. A. B. Roytsin.
JSC "MEDICAL UNIVERSITY OF ASTANA"
Department of Informatics and Mathematics with a course in Medbiophysics
abstract
Medbiophysics
Topic "Use of nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) in medical research"
The work was done by a student:
Faculty of General Medicine, Dentistry and Pharmacy
Checked the work:
I Introduction.
II Main part. EPR and NMR: the physical nature and the processes underlying these phenomena, application in biomedical research.
1) Electronic paramagnetic resonance.
a) The physical nature of the EPR.
b) Splitting of energy levels. Zeeman effect.
c) Electronic splitting. Superfine splitting.
d) EPR spectrometers: device and principle of operation.
e) Spin probe method.
f) Application of EPR spectra in medical and biological research.
2) Nuclear magnetic resonance.
a) The physical nature of NMR.
b) NMR spectra.
c) The use of NMR in biomedical research: NMR introscopy (magnetic resonance imaging).
III Conclusion. The value of medical research methods based on EPR and NMR.
I . Introduction.
For an atom placed in a magnetic field, spontaneous transitions between sublevels of the same level are unlikely. However, such transitions are carried out induced under the influence of an external electromagnetic field. A necessary condition is the coincidence of the frequency of the electromagnetic field with the frequency of the photon, which corresponds to the energy difference between the split sublevels. In this case, you can observe the absorption of the energy of the electromagnetic field, which is called magnetic resonance. Depending on the type of particles - carriers of the magnetic moment - electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) are distinguished.
II ... Main part. EPR and NMR: the physical nature and the processes underlying these phenomena, application in biomedical research.
1. Electronic paramagnetic resonance. Electron paramagnetic resonance (EPR) is the resonant absorption of electromagnetic energy in the centimeter or millimeter wavelength range by substances containing paramagnetic particles. EPR is one of the methods of radiospectroscopy. A substance is called paramagnetic if it does not have a macroscopic magnetic moment in the absence of an external magnetic field, but acquires it after the application of a field, while the magnitude of the moment depends on the field, and the moment itself is directed in the same direction as the field. From a microscopic point of view, the paramagnetism of a substance is due to the fact that the atoms, ions or molecules included in this substance have permanent magnetic moments randomly oriented relative to each other in the absence of an external magnetic field. The application of a constant magnetic field leads to a directional change in their orientations, which causes the appearance of a total (macroscopic) magnetic moment.
EPR was discovered by E.K. Zavoisky in 1944. Since 1922, in a number of works, considerations have been expressed about the possibility of the existence of EPR. An attempt to experimentally detect the EPR was undertaken in the mid-1930s by the Dutch physicist K. Gorter. However, EPR was observed only thanks to the radio spectroscopic methods developed by Zavoiskii. EPR is a special case of magnetic resonance.
The physical nature of the EPR. The essence of the phenomenon of electron paramagnetic resonance is as follows. If we place a free radical with the resulting angular momentum J in a magnetic field with a strength B 0, then for a nonzero J, the degeneracy is lifted in the magnetic field, and as a result of interaction with the magnetic field, 2J + 1 levels arise, the position of which is described by the expression: W \u003d gβB 0 M, (where М \u003d + J, + J-1,… -J) and is determined by the Zeeman interaction of the magnetic field with the magnetic moment J.
If now an electromagnetic field with a frequency ν is applied to the paramagnetic center, polarized in a plane perpendicular to the magnetic field vector B 0, then it will cause magnetic dipole transitions obeying the selection rule ΔM \u003d 1. When the energy of the electronic transition coincides with the photon energy of the electromagnetic wave, resonance absorption of microwave radiation will occur. Thus, the resonance condition is determined by the fundamental relation of magnetic resonance hν \u003d gβB 0.
Splitting energy levels. Zeeman effect. In the absence of an external magnetic field, the magnetic moments of the electrons are oriented in a random way, and their energy practically does not differ from each other (E 0). When an external magnetic field is applied, the magnetic moments of electrons are oriented in the field depending on the magnitude of the spin magnetic moment, and their energy level is split into two. The energy of interaction of the magnetic moment of an electron with a magnetic field is expressed by the equation:
, is the magnetic moment of the electron, H is the magnetic field strength. From the equation of the proportionality coefficient it follows that
,
and the energy of interaction of an electron with an external magnetic field will be
.
This equation describes the Zeeman effect, which can be expressed in the following words: the energy levels of electrons placed in a magnetic field are split in this field depending on the magnitude of the spin magnetic moment and the intensity of the magnetic field.
Electronic cleavage. Superfine splitting. Most applications, including biomedical ones, are based on the analysis of a group of lines (and not just singlents) in the EPR absorption spectrum. The presence in the EPR spectrum of a group of close lines is conventionally called splitting. There are two characteristic types of splitting for the EPR spectrum. The first, electronic splitting, occurs when a molecule or atom has not one, but several electrons that cause EPR. The second, hyperfine splitting, is observed when electrons interact with the magnetic moment of the nucleus. According to classical concepts, an electron orbiting a nucleus, like any charged particle moving in a circular orbit, has a dipole magnetic moment. Similarly in quantum mechanics, the orbital angular momentum of an electron creates a certain magnetic moment. The interaction of this magnetic moment with the magnetic moment of the nucleus (due to the nuclear spin) leads to hyperfine splitting (i.e., creates a hyperfine structure). However, the electron also has a spin that contributes to its magnetic moment. Therefore, hyperfine splitting exists even for terms with zero orbital angular momentum. The distance between the sublevels of the hyperfine structure is 1000 times smaller in order of magnitude than between the levels of the fine structure (this order of magnitude is essentially due to the ratio of the electron mass to the nuclear mass).
EPR spectrometers: design and principle of operation. The device of an EPR radio spectrometer is in many ways similar to the device of a spectrophotometer for measuring optical absorption in the visible and ultraviolet parts of the spectrum. The source of radiation in a radio spectrometer is a klystron, which is a radio tube that emits monochromatic radiation in the range of centimeter waves. The diaphragm of the spectrophotometer in the radio spectrometer corresponds to an attenuator, which makes it possible to dose the power incident on the sample. The cuvette with the sample in the radio spectrometer is located in a special unit called a resonator. The resonator is a parallelepiped with a cylindrical or rectangular cavity in which an absorbing sample is located. The dimensions of the resonator are such that a standing wave is formed in it. An element absent in an optical spectrometer is an electromagnet, which creates a constant magnetic field, which is necessary to split the energy levels of electrons. The radiation passed through the measured sample, in the radio spectrometer and in the spectrophotometer, enters the detector, then the detector signal is amplified and recorded on a recorder or computer. One more distinction of the radio spectrometer should be noted. It consists in the fact that radio frequency radiation is transmitted from the source to the sample and further to the detector using special rectangular tubes called waveguides. The dimensions of the section of the waveguides are determined by the wavelength of the transmitted radiation. This feature of the transmission of radio radiation through waveguides determines the fact that a constant radiation frequency is used to register the EPR spectrum in a radio spectrometer, and the resonance condition is achieved by changing the magnetic field. Another important feature of a radio spectrometer is signal amplification by modulating it with a high-frequency alternating field. As a result of signal modulation, its differentiation occurs and the absorption line transforms into its first derivative, which is an EPR signal.
Spin probe method. Spin probes are individual paramagnetic chemicals used to study various molecular systems using EPR spectroscopy. The nature of the change in the EPR spectrum of these compounds allows obtaining unique information about the interactions and dynamics of macromolecules and about the properties of various molecular systems. This is a method for studying molecular mobility and various structural transformations in condensed media using the electron paramagnetic resonance spectra of stable radicals (probes) added to the substance under study. If stable radicals are chemically bound to particles of the medium under study, they are called labels and speak of the method of spin (or paramagnetic) labels. Nitroxyl radicals are mainly used as probes and labels, which are stable in a wide temperature range (up to 100-200 ○ C), are able to enter into chemical reactions without loss of paramagnetic properties, and are readily soluble in aqueous and organic media. The high sensitivity of the EPR method allows the introduction of probes (in a liquid or vapor state) in small quantities - from 0.001 to 0.01% by weight, which does not cause changes in the properties of the objects under study. The spin probe and label method is used especially widely for the study of synthetic polymers and biological objects. In this case, it is possible to study the general laws governing the dynamics of low-molecular-weight particles in polymers, when spin probes simulate the behavior of various additives (plasticizers, dyes, stabilizers, initiators); receive information about changes in molecular mobility during chemical modification and structural and physical transformations (aging, structuring, plasticization, deformation); investigate binary and multicomponent systems (copolymers, filled and plasticized polymers, composites); study polymer solutions, in particular the effect of solvent and temperature on their behavior; determine the rotational mobility of enzymes, structure and spaces. the location of groups in the active center of the enzyme, the conformation of the protein under various influences, the rate of enzymatic catalysis; study membrane preparations (for example, to determine the microviscosity and the degree of ordering of lipids in the membrane, to study lipid-protein interactions, membrane fusion); study liquid crystal systems (the degree of order in the arrangement of molecules, phase transitions), DNA, RNA, polynucleotides (structural transformations under the influence of temperature and environment, the interaction of DNA with ligands and intercalating compounds). The method is also used in various fields of medicine to study the mechanism of action of drugs, analyze changes in cells and tissues in various diseases, determine low concentrations of toxic and biologically active substances in the body, and study the mechanisms of action of viruses.
INTRODUCTION …………………………………………………………………… .2
1.PRINCIPLE OF THE EPR METHOD ………………………………………………… ..3
1.1. The history of the discovery of the EPR method …………………………………………… ..3
1.2. Mechanical and magnetic moments of an electron ………………………… 4
1.3. Zeeman effect ... ... ... ... ............................................ ................................... 6
1.4. The basic resonance equation …………………………………………… 8
2. CHARACTERISTICS OF EPR SPECTRA ………………………………… .10
2.1. Signal amplitude, line shape and line width …………………… .10
2.2. Hyperfine structure of EPR spectra ………………………………… .16
……………………………………………………………..18
3. DEVICE OF THE EPR RADIOSPECTROMETER …………………… ... 22
4. APPLICATION OF EPR IN MEDICAL AND BIOLOGICAL RESEARCH …………………………………………………………… .24
4.1. EPR signals observed in biological systems ……………… ..24
4.2. Spin label and probe method ………………………………………… 26
4.3. Spin trap method …………………………………………… ... 35
CONCLUSION ………………………………………………………… ... 39
LIST OF USED SOURCES ……………………… ..40
INTRODUCTION
Electronic paramagnetic resonance (EPR, electron spin resonance), the phenomenon of resonant absorption of electromagnetic radiation by paramagnetic particles placed in a constant magnetic field, caused by quantum transitions between the magnetic sublevels of paramagnetic atoms and ions (Zeeman effect). OpenZavoisky Evgeny Konstantinovich in Kazan State University in 1944
In the absence of a constant magnetic field H, the magnetic moments of the unpairedelectrons directed arbitrarily, the state of the system of such particles is degenerate in energy. When the field H is superimposed, the projections of the magnetic moments on the direction of the field take on certain values \u200b\u200band the degeneracy is removed (the Zeeman effect), i.e., the energy level splitselectrons E 0.
Since on the lower level the numberelectrons more in accordance with the Boltzmann distribution, then mainly resonant absorption of the energy of the alternating magnetic field (its magnetic component) will occur.
For continuous observation of energy absorption, the resonance condition is insufficient, since when exposed to electromagnetic radiation, the populations of the sublevels will become equal (saturation effect). To maintain the Boltzmann distribution of the populations of the sublevels, relaxation processes are required.
The main parameters of the EPR spectra are the intensity, shape and width of the resonancelines , g-factor, constants of fine and hyperfine (HFS) structure.
1.PRINCIPLE OF THE EPR METHOD
1.1 History of the EPR method discovery
Electron paramagnetic resonance method (EPR, EPR -electron paramagnetic resonance, ESR - electron spin resonance ) is the main method for learningparamagnetic particles. To paramagnetic particles with an important biologicalmeaning are two main types - these are free radicals and metal complexesvariable valence (such as Fe, Cu, Co, Ni, Mn).
The method of electron paramagnetic resonance was discovered in 1944 by E.K. Zavoisky in the study of the interaction of microwave electromagnetic radiation with metal salts. He noticed that a CuCl2 single crystal, placed in a constant magnetic field of 40 Gauss (4 mT), can absorb radiation with a frequency of about 133 MHz.
The pioneers of the use of EPR in biological research in the USSR were L.A. Blumenfeld and A.E. Kalmanson, who began to study free radicals of proteins obtained by ionizing radiation.
Over time, the synthesis of stable nitroxyl radicals has significantly expanded the scope of the EPR method in biological and medical research. Today this method is one of the most widely used methods of modern science.
1.2. Mechanical and magnetic moments of an electron
The EPR method is based on the absorption of radio frequency electromagnetic radiation by unpaired electrons in a magnetic field.
It is well known that an electron in an atom participates in orbital and spin motion, which can be characterized by the corresponding mechanical and magnetic moments. So, the orbital magnetic moment is associated with the mechanical expression
(1)
where is the magnetic orbital moment, and is the mechanical orbital moment. In turn, the mechanical orbital moment can be expressed in terms of the orbital quantum number
(2)
Substituting expression (1.2) into (1.1), we obtain that
The quantity is an elementary magnetic moment and is called the Bohr magneton for an electron. It is denoted by the letter β and is equal to 9.27 · 10-24 J / T.
For the spin magnetic moment, we can write similar expressions
(4)
(5)
(6)
where is the spin magnetic moment,Ps - mechanical magnetic moment, ands –Spin quantum number. It is important to note that the coefficient of proportionality between andPs (e / m ) is twice as large as for andPl (e / 2m).
As a result, the total magnetic moment of the electron, which is a vector, will be equal to the sum of the vectors of the orbital and spin magnetic moments
(7)
Since the absolute values \u200b\u200bof and can differ greatly, for the convenience of taking into account the contribution of the orbital and spin magnetic moments to the total magnetic moment of the electron, a proportionality coefficient is introduced showing the fraction of each ofmoments in the total magnetic moment - the valueg or g factor.
where Pj Is the total mechanical moment of the electron, equal toPl + Ps. g -Factor is equal to one ats \u003d 0 (i.e., in the absence of spin motion) and is equal to two if the orbital angular momentum is zero (l \u003d 0). g - The factor is identical to the Lande spectroscopic splitting factor and can be expressed in terms of the total quantum numbersS, P and J:
where (9)
Since in most cases electron orbitals are very different from spherical ones, the orbital magnetic moment makes a relatively small contribution to the total magnetic moment. To simplify calculations, this contribution can be neglected. In addition, if we replace the spin mechanical moment with its projection onto the preferred direction (for example, on the direction of the magnetic field), then we get the following expression:
(10)
where eh / 4πm is the Bohr magneton, and is the magnetic quantum number, which is the projection of the spin magnetic moment onto the preferred direction and is equal to ± 1/2.
1 .3. Zeeman effect
Figure 1 - The orientation of electrons in an external magnetic field (H).
In the absence of an external magnetic field, the magnetic moments of the electrons are oriented randomly (Fig. 1 on the left), and their energy practically does not differ from each other (E0). When an external magnetic field is applied, the magnetic moments of electrons are oriented in the field depending on the magnitude of the spin magnetic moment (Fig. 1, right), and their energy level is split into two (Fig. 2).
Figure 2 - Splitting of energy levels of single electrons in a magnetic field (Zeeman effect).
The energy of interaction of the magnetic moment of an electron with a magnetic field is expressed by the equation
(11)
where μ is the total magnetic moment of the electron,H Is the magnetic field strength, and cos (μH) is the cosine of the angle between vectors μ and H.
In our case, the energy of interaction of an electron with an external magnetic field will be
(12)
and the difference in energy between the two levels is
(13)
Thus, the energy levels of electrons placed in a magnetic field are split in this field, depending on the magnitude of the spin magnetic moment and the intensity of the magnetic field (zeeman effect).
1.4 Basic resonance equation
The number of electrons in the system under study, having this or that energy, will be determined in accordance with the Boltzmann distribution, namely
(14)
where is the number of electrons at a higher or lower energy level corresponding to the magnetic moment of an electron with spin +1/2 or –1/2.
If an electromagnetic wave is incident on a system of electrons in a magnetic field, then at certain values \u200b\u200bof the energy of the incident quanta, transitions of electrons between levels will occur.
A necessary condition is the equality of the incident quantum energy (hν) and the energy difference between the levels of electrons with different spins (gβH).
ΔE \u003d hν \u003d gβH (15)
This equation expresses the main condition for the absorption of energy by electrons and is calledthe basic resonance equation... Under the influence of radiation, electrons at a higher energy level will emit energy and return to a lower level, this phenomenon is called induced emission. Electrons at the lower level will absorb energy and move to a higher
energy level, this phenomenon is calledresonant absorption... Since the probabilities of single transitions between energy levels are equal, and the total transition probability is proportional to the number of electrons at a given energy level, the absorption of energy will prevail over its radiation. This is due to the fact that, as follows from the Boltzmann distribution, the population of the lower level is higher than the population of the upper energy level.
It should be remembered that the difference in the energy levels of an electron in a magnetic field (as well as other charged particles with spin, for example, protons) is associated with the presence of an electron's own magnetic moment. Paired electrons have compensated magnetic moments, and they do not react to an external magnetic field; therefore, ordinary molecules do not give EPR signals. Thus, EPR allows you to detect and study the propertiesfree radicals(having an unpaired electron in outer orbitals) and metal complexes of variable valence (in which the unpaired electron belongs to deeper electron shells). These two groups of paramagnetic particles are often referred to as paramagnetic centers.
2 CHARACTERISTICS OF EPR SPECTRA
The EPR method allows us to study the properties of paramagnetic centers through the absorption spectra of electromagnetic radiation by these particles. Knowing the characteristics of the spectra, one can also judge the properties of paramagnetic particles. The main characteristics of the spectra include amplitude, line width, line shape,g -factor and hyperfine structure of spectra.
2.1. Signal amplitude, line shape and line width
Signal amplitude
The EPR signal is the first derivative of the absorption spectrum (Fig. 3). The area under the absorption line is proportional to the concentration of paramagnetic particles in the sample. Thus, the concentration of paramagnetic centers is proportional to the first integral under the absorption line or the second integral of the EPR spectrum. If two signals have the same width, then the concentrations of paramagnetic centers are related as the amplitudes of the signals in the absorption spectra.
Figure 3 - EPR signal. Left - dependence of microwave absorption on the magnetic field strength (H); on the right is the first derivative of this relationship. EPR spectrometers record curves of the second type.
To determine the concentration, the areas under the absorption curve are measured for a reference sample with a known concentration of paramagnetic centers and for a measured sample, and the unknown concentration is found from the proportion, provided that both samples have the same volume:
(16)
where and are the concentrations of the measured sample and the reference sample, respectively, andS x and S 0 - areas under the absorption lines of the measured signal and the reference sample.
To determine the area under the absorption line of an unknown signal, you can use the numerical integration technique
(17)
where f "(H ) Is the first derivative of the absorption line (EPR spectrum),F (H ) Is the absorption line function, andH - magnetic field strength.
(18)
Considering that F (H). H at the points -∞ and ∞ is equal to zero anddF (H) is equal to f "(H) dH, we get
(19)
where f "(H ) Is the first derivative of the absorption line, or the EPR spectrum. It is easy to pass from the integral to the integral sum, taking into account thatH \u003d nΔH, we get
(20)
where Δ H Is the step of changing the magnetic field, andn i - step number. Thus, the area under the absorption curve will be equal to the product of the square of the magnitude of the magnetic field step by the sum of the products of the EPR spectrum amplitude by the step number. From expression (20) it is easy to see that at largen (i.e., far from the center of the signal), the contribution of the distant parts of the spectrum can be quite large even at small values \u200b\u200bof the signal amplitude.
Line shape
Although, according to the main resonance equation, absorption occurs only when the energy of the incident quantum is equal to the energy difference between the levels of unpaired electrons, the EPR spectrum is continuous in some vicinity of the resonance point. The function that describes the RCS signal is called the line shape function. In dilute solutions, when the interaction between paramagnetic particles can be neglected, the absorption curve is described by the Lorentz function:
(21)
where is the function of the absorption curve at the resonance point, is the field value at the resonance point, and is the signal width at half maximum. Similar designations are used for the absorption curve described by the Gaussian function.
(22)
The Gaussian function is the envelope of the EPR spectrum if there is interaction between the paramagnetic particles. The shape of the line is especially important when determining the area under the absorption curve. As can be seen from the above formulas, the Lorentzian line has a slower decay and, accordingly, wider wings, which can give a significant error when integrating the spectrum.
Line width
The width of the EPR spectrum depends on the interaction of the magnetic moment of the electron with the magnetic moments of the surrounding nuclei (lattice) (spin-lattice interaction) and electrons (spin-spin interaction). In the absence of these interactions, the energy absorbed by the electrons would lead to a decrease in the difference between the level populations and the termination of absorption.
However, in the experiment, the change in the level population difference is not observed due to the fact that there are processes in which the absorbed energy is transferred to the environment and the electrons return to the initial level. Such processes are called relaxation processes; they maintain a constant difference in the population of the energy levels. The relaxation mechanism consists in the transfer of the electromagnetic energy of a quantum to the lattice or surrounding electrons and the return of the electron to
low energy level. The time during which the electron remains at a high energy level is called the relaxation time. Accordingly, there is a spin-lattice time (T 1) and spin-spin (T 2) relaxation.
One of the reasons for the broadening of absorption bands in EPR signals lies in the wave properties of elementary particles, which are manifested in the existence of the well-known Heisenberg uncertainty relation principle. According to this principle, the more precisely the observation time is specified (the less Δt ), the greater the uncertainty in the value of the particle energy (:
(23)
If we assume that Δt it's relaxation timeT, and Δ E corresponds to g βΔ H , then we get that
(24)
those. the uncertainty in the linewidth is inversely proportional to the relaxation time. The observed relaxation time is considered the sum of the spin-lattice and spin-spin relaxation times.
(25)
Free radicals in solutions have T1 \u003e\u003eT 2, therefore the line width will depend mainly on T2.
The “natural” broadening of the EPR signal, which depends on the time of spin-lattice and spin-spin relaxation, is not the only mechanism that affects the linewidthc ignored. Also importantdipole-dipole interaction; anisotropy g -factor a; dynamic line broadening and spin exchange.
At the heart of dipole-dipole interaction lies the interaction of the magnetic moment of an unpaired electron with a local magnetic field created by neighboring electrons and nuclei. The magnetic field strength at the point where the unpaired electron is located depends on the mutual orientation of the magnetic moments of the unpaired electron and another electron or nucleus and the distance between these centers. The change in the energy of an unpaired electron is determined by the equation
(26)
where μ is the magnetic moment of the electron, θ is the angle between the interacting magnetic momentsR - the distance between them.
Contribution g-factor anisotropyin the broadening of the EPR line is due to the fact that the orbital motion of the electron creates a magnetic field with which the spin magnetic moment interacts. This creates a shift in the magnitude of the external field strength at which resonance is observed, i.e. to the shift of the position of the maximum of the EPR signal. In turn, this manifests itself in an apparent deviationg -factor of a free electron from 2.00. On the other hand, the effect of the orbital magnetic field on the electron
depends on the orientation of the molecule with respect to the external magnetic field, which leads to a broadening of the EPR signal when measured in a system consisting of many chaotically oriented molecules.
The broadening of the EPR signal can also be associated with the mutual transformation of two paramagnetic particles. So, if each of the particles has its own EPR spectrum, then an increase in the rate of mutual transformation into each other will lead to line broadening, since in this case, the lifetime of the radical in each state decreases. Such a changesignal width is calleddynamic broadening signal.
Spin exchange is another reason for the broadening of the EPR signal. The mechanism of signal broadening during spin exchange consists in changing the direction of the spin magnetic moment of the electron to the opposite one upon collision with another unpaired electron or other paramagnet. Since such a collision decreases the lifetime of an electron in a given state, again the EPR signal broadens. The most frequent case of EPR line broadening by the mechanism of spin exchange is signal broadening in the presence of oxygen or paramagnetic metal ions.
2.2 Hyperfine structure of EPR spectra
The splitting of a single EPR line into several is based on the phenomenonhyperfine interaction, i.e., the interaction of the magnetic moments of unpaired electrons () with the magnetic moments of neighboring nuclei (
Figure 4 gives an explanation of the hyperfine interaction. An unpaired electron in a radical can be located close to a proton, for example, as in an ethanol radical (1). In the absence of the influence of nearby protons, the electron has a signal in the form of a single line (2). However, the proton also has a magnetic moment, which is oriented in an external magnetic field (H 0) in two directions (along the field or against the field) because, like an electron, it has a spin number S \u003d ½. Being a small magnet, the proton creates a magnetic field, which at the location of the electron has certain values \u200b\u200bof + Hp or –Hp, depending on the orientation of the proton (3). As a result, the total magnetic field applied to an unpaired electron (4) has a value slightly larger (+ Hp) or slightly less (- Hp) than in the absence of a proton (). Therefore, the EPR signal of the radical consists of two bands, the distance from which to the former center of the band is Hp (5).
Figure 4- Ultrafine splitting of the EPR signal in the ethanol radical.
1 - ethanol radical. 2 - EPR signal of an electron in an external field. 3 - orientation of protons in an external magnetic field. 4 - increase or decrease in the field acting on the electron as a result of the imposition of the magnetic field of the proton (H p) to an external magnetic field. 5 - EPR signal of the radical, in which the magnetic field of the proton is superimposed on the external magnetic field.
In our example, the spin of a nucleus interacting with an unpaired electron was ± 1/2, which ultimately gave us a splitting into two lines. This spin is typical for protons. The nuclei of nitrogen atoms (N14) have spininteger ... It can take values \u200b\u200b± 1 and 0. In this case, when an unpaired electron interacts with the nucleus of a nitrogen atom, splitting into three identical lines corresponding to the spin values \u200b\u200b+1, –1, and 0 will be observed. In the general case, the number
lines in the EPR spectrum is 2m N + 1. (see below, fig. 10)
Naturally, the number of unpaired electrons and, accordingly, the area under the EPR absorption curve are independent of the nuclear spin and are constant values. Consequently, when a single EPR signal is split into two or three, the intensity of each component will be 2 or 3 times lower, respectively.
A very similar picture arises if an unpaired electron interacts not with one, but with several equivalent (with the same hyperfine interaction constant) nuclei that have a magnetic moment different from zero, for example, two protons. In this case, there are three states corresponding to the orientation of the proton spins: (a) both along the field, (b) both against the field, and (c) one along the field and one against the field. Option (c) is twice as likely as (a) or (b), because can be done in two ways. As a result of such a distribution of unpaired electrons, a single line will split into three with an intensity ratio of 1: 2: 1. In general, forn equivalent nuclei with spin mN, the number of lines isn 2 m N +1.
2.3. Properties of atoms with magnetic nuclei, constants, HFC of an unpaired electron with a nucleus
|
Atom |
Mass number |
Nuclear spin |
a x 10- 4 T |
|
|
99,98 |
||||
|
7,52 |
54,29 |
|||
|
92,48 |
143,37 |
|||
|
316,11 |
||||
|
93,26 |
82,38 |
|||
|
72,15 |
361,07 |
|||
|
27,85 |
1219,25 |
|||
|
819,84 |
IN - electronic systems (most organic free radicals)spin density at the point of the nucleus is equal to zero (the nodal point of the p-orbital) and two mechanisms of the appearance of HFC (spin transfer) are realized: configurational interaction and the effect of superconjugation. The mechanism of configurational interaction is illustrated by considering the CH fragment (Fig. 5). When an unpaired appears on the p-orbitalelectron , its magnetic field interacts witha pair of electrons -bonds С - Н so that their partial unpairing (spin polarization) occurs, as a result of which onproton negativespin densitysince the interaction energiesspins and are different. The state shown in fig. 5, a, is more stable, since for carbonatom carrying unpairedelectron , in accordance withhund rule maximummultiplicity... For systems of this type, there is a relationship between the CTB constant withproton and spin density on the appropriate carbonatom determined by the McConnell ratio: where Q \u003d -28 x 10 -4 T, - spin density on a carbon atom ... Spin transfer by the configuration interaction mechanism is realized for aromaticprotons and -protons in organic free radicals.
Figure 5 - Possible spin configurations for-orbital connectinghydrogen atom in the fragment C - H, and p-orbitalcarbon atom with spin a - spin on the bonding -orbitals and p-orbitalscarbon atom parallel, b - the sameback antiparallel.
The over-conjugation effect is to directly overlapunpaired electron orbitals and magnetic cores. In particular, in alkyl radicals, HFC arises by this mechanism on the nuclei-protons. For example, in the ethyl radical on-protons HFC is determined by the configuration interaction, and on-protons - by superconjugation. Equivalence of CTB with threeprotons methyl group in this case is due to the rapid rotation of the CH3 with respect to the С - С bond. In the absence of free rotation (or in the case of hindered rotation), which is realized in the liquid phase for many systems with branched alkyl substituents or in single crystal samples, the CTB constant with-protons is determined by the expression where - dihedral angle between 2pz-orbital of the -carbon atom and the CH bond, B 0 4 x 10 -4 T determines the contribution of the spinpolarization along the nuclear core (configuration interaction), B2 45 x 10 -4 T. In the limit of fast rotation ah \u003d 2.65 x 10- 3 T. In spectroscopy EPR of triplet states (S \u003d 1) in addition to electron-nuclear interactions (HFC), it is necessary to take into account the interaction of unpairedelectrons together. It is determined by the dipole-dipole interaction averaged to zero in the liquid phase and described by the parameters of zero splitting D and E, which depend on the distance between unsavedelectrons (radical couples), andexchange interaction (isotropic) due to direct overlaporbitals of unpaired electrons (spin exchange), which is described by the exchange integral Jexchange For biradicals , in which each of the radical centers has one magnetic nucleus with the HFC constant on this nucleus a, in the case of fast (strong) exchange Jexchange a, and every unpairedelectron of the biradical system interacts with the magnetic nuclei of both radical centers. With weak exchange (Jexchange a) EPR spectra of each radical center are recorded independently, that is, a "monoradical" picture is recorded. Dependency Jexchange from t-ry and solvent allows you to get the dynamic characteristics of the biradical system (frequency and energy barrier of spin exchange).
- EPR RADIOSPECTROMETER DEVICE
The device of an EPR radio spectrometer only vaguely resembles the device of a spectrophotometer for measuring optical absorption in the visible and ultraviolet parts of the spectrum (Fig. 6).
Figure 6 - EPR spectrometer device.
The source of radiation in a radio spectrometer is a klystron, which is a radio tube that emits monochromatic radiation in the range of centimeter waves.
The role of the diaphragm in the radio spectrometer is played by an attenuator, which makes it possible to dose the power incident on the sample. The cuvette with the sample in the radio spectrometer is located in a special unit called a resonator. The resonator is a hollow parallelepiped made of metal, the cavity of which has a cylindrical or rectangular shape. It contains an absorbing sample. The dimensions of the resonator are such that the incoming radiation forms a standing electromagnetic wave in it. An element that is completely absent in an optical spectrometer is an electromagnet, which creates a constant magnetic field necessary to split the energy levels of electrons. The radiation that has passed through the sample being measured enters the detector, then the detector signal is amplified and registered on a recorder or computer. The peculiarity of the design of the radio spectrometer lies in the fact that the radiation of the radio range is transmitted from the source to the sample and further to the detector using special rectangular tubes that serve as waveguides. The dimensions of the section of the waveguides are determined by the wavelength of the transmitted radiation. This feature of the transmission of radio radiation through waveguides determines the fact that a constant radiation frequency is used to register the EPR spectrum in a radio spectrometer, and the resonance condition is achieved by changing the magnetic field.
Another important feature of the radio spectrometer is that it does not measure the absorption (A) of electromagnetic (microwave) waves, but the first derivative of absorption with respect to the magnetic field strength dA / dH. The point is that to measure the absorption, it is necessary to compare the intensities of the transmitted radiation between the measured and the control object (say, an empty cuvette), and when measuring the first derivative, the control object is not needed. When the magnetic field changes, the intensity of microwave waves passing through empty space or a non-absorbing object does not change and the first derivative of absorption is equal to zero. If microwave waves pass through an object with paramagnetic centers, then absorption takes place, and its magnitude depends on the strength of the magnetic field. We change the field and the absorption changes, which manifests itself in a change in the intensity of the measured microwave vibration. It is this change in the intensity of the measured microwave with a slight modulation of the magnetic field about a given value that makes it possible to determine dA / dH at each point of H, thereby obtaining spectra, or EPR signals.
- APPLICATION OF EPR IN MEDICAL AND BIOLOGICAL RESEARCH
- EPR signals observed in biological systems
The use of the EPR method in biological research is associated with the study of two main types of paramagnetic centers - free radicals and metal ions of variable valence. The study of free radicals in biological systems is associated with the difficulty in the low concentration of free radicals formed during the life of cells. According to various sources, the concentration of radicals in normally metabolizing cells is approximately M, while modern radio spectrometers allow measuring the concentration of M radicals. The concentration of free radicals can be increased by inhibiting their death or increasing the rate of their formation. Under experimental conditions, the formation
radicals are most easily observed when biological objects are irradiated at a very low temperature (say 77K) in the course of their irradiation with UV or ionizing radiation. The study of the structure of radicals of more or less complex biologically important molecules obtained under such conditions was one of the first areas of application of the EPR method in biological research (Fig. 7). The second direction of application of the EPR method in biological research was the study of metals of variable valence and / or their complexes existingin vivo ... Due to the short relaxation times, the EPR signals of metalloproteins can also be observed only at low temperatures, for example, the temperature of liquid nitrogen or even helium.
Figure 7 - EPR spectra of UV-irradiated cysteine \u200b\u200bat liquid nitrogen temperature (77 K) and normal temperature (300 K).
As an example, Fig. 8 shows the EPR spectrum of rat liver. On it you can see the signals of cytochrome P-450, which haveg -factor 1.94 and 2.25, the signal of methemoglobin withg - factor 4.3 and the signal of free radicals belonging to the semiquinone radicals of ascorbic acid and flavins withg-factor 2.00.
Figure 8 - EPR spectrum of rat liver.
However, EPR signals of some radicals can also be observed at room temperature. Such signals include EPR signals of many semiquinone or phenoxyl radicals, such as the semiquinone radical of ubiquinone, phenoxyl and semiquinone radicals of α-tocopherol (vitamin E), vitamin D, and many others (Fig. 9).
Figure 9 - EPR signals of semiquinone and phenoxyl radicals.
- Spin label and probe method
The synthesis of stable free radicals has become an important stage in the development of the use of the EPR method in biological research. Among these radicals, the most popular are nitroxyl radicals.
The stability of nitroxyl radicals is due to spatial screening of the N – O group. having an unpaired electron, four methyl groups that prevent the reaction with the participation of free valence. However, this screening is not absolute and the free valence restoration reaction can still occur. Ascorbic acid, for example, is a good reducing agent for nitroxyl radicals.
The EPR spectrum of nitroxyl radicals usually consists of three lines of equal intensity due to the interaction of an unpaired electron with the nucleus of a nitrogen atom (Fig. 10).
Figure 10 - Formula and EPR spectrum of nitroxyl radical 2,2,6,6-
tetramethylpiperidine-1-oxyl (TEMPO).
Let's leave aside the complicated theory explaining the dependence of the EPR signal shape on the probe mobility and confine ourselves to a very schematic presentation of what is observed in experiments. If the nitroxyl radical is in an aqueous solution, then its rotation is isotropic and rather fast, and an EPR signal is observed, consisting of three narrow symmetric lines (Fig. 11, top). With a decrease in the rotation rate, broadening of the lines and a change in the amplitude of the spectrum components are observed (Fig. 11, in the middle). A further increase in the viscosity of the medium leads to an even greater change in the EPR signal of the spin probe (Fig. 11, bottom).
To quantitatively describe the rotational motion of the radical, the concept of the rotational correlation time (τс) is used. It is equal to the time of rotation of the nitroxyl radical through the angle π / 2. Based on the analysis of the EPR signal, the correlation time can be estimated using the empirical equation
(27)
Where Δ is the bandwidth of the EPR spectrum at a low value of the field, and and is the intensity of the high-field and low-field components of the EPR spectrum. This equation can be used with a correlation time of 5 · to s.
The synthesis of stable nitroxyl radicals of the TEMPO family was an important stage in the use of the EPR method to study the internal viscosity of biological membranes and proteins for solving biomedical problems.
Figure 11 - EPR spectrum of TEMPO at different times of rotational correlation τс (numbers to the left of the spectra).
However, the TEMPO derivatives have, unfortunately, one significant drawback - due to their amphiphilicity, it is difficult to determine the localization of this probe and thus answer the question of where we, in fact, determine the microviscosity. This problem was practically solved when the so-called "fatty acid spin probes" appeared, i.e. compounds in which the nitroxyl radical molecule was covalently attached to the fatty acid molecule. In this case, the EPR spectrum undoubtedly reflects the properties of the hydrophobic (lipid) phase of the system under study, where the probe is placed. Figure 12 shows a schematic structure of a fatty acid spin probe, 5-doxyl stearate, in which a nitroxyl radical (doxyl, a compound related to TEMPO in structure) is attached to the 5th carbon atom of a stearic acid molecule. The characteristic of the motion of such a probe is a quantity called the ordering parameterS , which characterizes the degree of asymmetry of the probe rotation relative to the longitudinal and transverse axes of its molecule. The ordering parameter can be found from the characteristics of the EPR spectrum using the empirical equation
(28)
where A || and A ⊥ - the parameters indicated in the figure. Theoretically, the ordering parameter can vary from 0 to 1, with a change in the viscosity and structure of the membrane. With perfectly symmetric rotation, when the speed of rotation around three axes is the same (which is typical for spherical particles in an isotropic medium), the order parameter is zero. The ordering parameter is 1 if the axis of rotation of the probe coincides with the normal to the membrane, and there is no rotation with respect to other axes. At low temperatures or in membranes made of synthetic saturated phospholipids, the rotation of the probe rotates mainly around the long axis of the molecule, oriented across the membrane. In this case, the ordering parameter has high values. With decreasing membrane viscosity, the value of the ordering parameter decreases.
Figure 12 - Chemical formula and EPR spectrum of 5 - doxyl stearate.
A very valuable feature of spin probes containing a fatty acid is the ability to measure the ordering parameter at different distances from the membrane surface, the so-called ordering profile or viscosity profile. For this, a set of spin probes is used, which are molecules of the same fatty acid, which contain a nitroxyl fragment at different distances from the carboxyl group. For example, spin probes with a nitroxyl radical at the 5th, 7th, 12th and 16th carbon atoms of stearic acid are used. A set of these compounds makes it possible to measure the S parameter at a distance of 3.5, 5, 8.5 and 10.5 angstroms from the membrane surface (Fig. 13).
Figure 13 - Change in the EPR signal when the nitroxyl radical is removed from the polar carboxyl group of the fatty acid.
Typically, the EPR spectra of a spin probe incorporated in a membrane and a probe in an aqueous solution may differ significantly. This property has been used to create a new class of spin probes that measure the interfacial potential of a membrane (often called surface potential). To measure this potential, the water / membrane partition coefficient of the neutral and charged probes is measured. Since the charged probe interacts with charges located on the membrane surface, its distribution coefficient will differ from that of the neutral probe. The distribution ratio is a measure of the surface potential of the membrane under study. The chemical formula of the spin probe used to measure the surface potential is shown in Fig. 14.
Figure 14 - Chemical formula of a charged spin probe.
Another important application of the spin probe method is the measurement of pH in microvolumes, for example, inside lysosomes or phagosomes of cells. For these purposes, special pH-sensitive spin probes are used (Fig. 15). The spin probe pH meter is based on the ability of the probe to give different EPR spectra in
protonated and deprotonated forms. Thus, depending on the pK of the spin probe, there is a certain pH range in which it is protonated and the corresponding change in the EPR spectrum occurs (Fig. 16).
Figure 15 - Chemical formulas of a pH-sensitive spin probe.
Figure 16 - EPR spectra and dependence of the concentration of the deprotonated pH-sensitive spin probe on pH
Everything that has been said so far in this section has been related tospin probe method... However, no less interesting isspin label method... The spin label method is based on the same principle of changing the EPR spectrum of a nitroxyl radical depending on the speed and isotropy of its rotation. The difference between the method is the fact that the spin label is covalently bound to another, more or less large
molecule.
One of the first and most successful applications of the spin labeling method was to measure the number and availability of SH-groups of proteins (Fig. 17). The chemical formula and EPR spectrum of the spin label interacting with sulfhydryl groups in the free state and after attachment to the protein are shown in Fig. 18.
Figure 17 - Scheme of interaction of the spin probe with the thiol group of the protein.
It can be seen from the figure that the EPR spectra of the spin label in the free and bound states are very different, which is associated with the difference in the speed and direction of rotation. Naturally, the bound spin label has a much lower rotation rate than in the free form. Moreover, the number of bound spin labels and, accordingly, the intensity of the EPR signal is proportional to the amount
sulfhydryl groups reacted with a spin label, which makes it possible to determine not only the mobility of the probe, but also its amount.
Figure 18 - Chemical formula of the spin label for SH-groups and the EPR spectra of the immobilized (1), bound (2) and free (3) spin labels.
Currently, there are many methodological techniques that allow one to study the topography of a protein globule using spin labels. Since many metal ions of variable valence are paramagnets and, in addition, can be located in the active center of the enzyme, the interaction of a spin label attached, for example, to a cysteine \u200b\u200bor histidine residue of a protein globule, with a metal ion will lead to a broadening of the EPR spectrum as a result of dipole-dipole interaction paramagnets.
- Spin trap method
The appearance of nitroxyl radicals turned out to be a decisive event in solving the problem of detecting and studying free radicals formed in living systems. The detection of radicals became possible thanks to the advent of the method
spin traps. The essence of the method is that some compound that is not a nitroxyl radical, but has a structure close to the nitroxyl radical (spin trap), interacts with a free, short-lived radical and turns into a long-lived nitroxyl radical (spin adduct ), the EPR spectrum of which is unique for a given radical or a family of radicals.
By their chemical nature, spin traps can be classified into two main classes: nitrons and nitroso compounds. The two most popular spin traps belong to nitrons - C-phenyl-N-tert-butyl nitrone (PBN) and 5,5-dimethyl-pyrroline-1-oxyl (DMPO). The reaction between PBN and a radical is as follows:
The stability of the resulting nitroxyl radical PBN (spin adduct) is explained by the fact that the oxygen atom, on which the unpaired electron is localized, is spatially screened by three methyl groups. The spin adduct of a radical has a unique EPR spectrum (see Fig. 19). In this case, the shape of the EPR spectra of spin adducts depends on the nature of the added free radical. Thus, it is possible to study free radical reactions in biological objects by the EPR method at physiological temperatures.
Figure 19 - EPR spectrum of the spin adduct and the values \u200b\u200bof the hyperfine splitting constants for some radicals.
aH and aN are the hyperfine splitting constants for a proton and a nitrogen atom, respectively
Figure 20 - Scheme of the reaction of the trap of DMPO and OH radical.
In fig. 20 shows the reaction of another spin trap, DMPO, with a hydroxyl radical and the formation of a spin adduct of this radical. Again, by measuring the hyperfine splitting constants of the spin adduct spectrum, one can identify the short-lived radical.
The spin trap method occupies one of the most important places in biomedical research, because allows you to detect and identify radicals formed in living cells and tissues. Such radicals include superoxide and hydroxyl radicals, as well as nitric oxide. In addition, the use of the spin trap method makes it possible to study the antioxidant properties of substances and the value of the antioxidant reserve.
CONCLUSION
The method of electron paramagnetic resonance (EPR) is based on the interaction of a substance with a magnetic field. As the name of the method suggests, it is used to study paramagnetic particles.
It is known that when paramagnets are placed in a magnetic field, the paramagnet is drawn into this field. This is due to the presence of magnetic moments in paramagnets. Magnetic moments are created by unpaired electrons.
Examples of paramagnetic particles of interest to biologists are free radicals, which are intermediate products of biochemical reactions, ions of metals of variable valence, such as iron, copper, manganese, etc.
The manifestation of the magnetic moment of the electron is due to the fact that the electron is a charged particle, and when the electron rotates around its axis (spin motion), a magnetic field appears directed along the axis of rotation. When a paramagnetic sample is placed in a magnetic field, the magnetic moments of unpaired electrons are oriented in this
field, similar to how it happens with magnetic arrows.
The magnetic moment of an unpaired electron in an external magnetic field can be oriented in two ways - along the field and against the field. Thus, if there are unpaired electrons in the system under study, the imposition of an external magnetic field leads to the separation of electrons into groups: the magnetic moments of some electrons are oriented along the field, others - against.
LIST OF USED SOURCES
- D. Ingram Electron paramagnetic resonance in biology [Text]. Publishing house "Mir", 1972.
- Free radicals in biological systems [Text]. vol. 1, art. 88-175, 178-226. Publishing house "Mir", 1979.
3. J. Wertz and J. Bolton, Theory and practical applications of the EPR method [Text], Moscow: Mir, 1975.
4. Modern methods of biophysical research [Text]. Workshop on Biophysics, edited by A.B. Rubin, Moscow: Higher School, 1988.
5. Method of spin labels [Text]. Theory and Application, edited by L. Berliner, Moscow: Mir, 1979.
6. A. N. Kuznetsov, Spin Probe Method, Moscow [Text]: Nauka, 1976.
7. V.E. Zubarev, Method of spin traps, Moscow [Text]: Moscow State University Publishing House, 1984.
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