Application of ESR spectroscopy. Electron paramagnetic resonance (EPR) EPR spectra

The EPR method has gained great importance in chemistry, physics, biology, and medicine, since it allows one to determine the structures and concentrations of organic and inorganic free radicals. Free radicals can be created chemically, photochemically, or by exposure to high energy radiation.

The EPR spectrum is produced by free radicals, molecules with an odd number of electrons, triplet states of organic molecules, paramagnetic ions of transition metals and their complexes.

The EPR method began to be used in biological research in the 50s of the 20th century. Due to its fairly high sensitivity and ability to determine the nature of paramagnetic particles, this method has found wide application for studying a number of biological processes.

In addition to free radical signals, a number of metal signals (Fe, Cu, Mn, Ni, Co) are observed in tissues. These metals are part of metalloproteins, which take part in a number of enzymatic processes. Iron-containing proteins (cytochromes, ferredoxins) are components of electron transport chains in mitochondria and chloroplasts.

A number of enzymatic systems have been studied using the EPR method, and free radical products of substrates have been discovered. In a number of cases, it turned out to be possible to observe the redox transformations of metal ions included in the active center of the enzyme.

EPR spectroscopy is widely used in studies of photosynthesis: the mechanism of the primary stages of charge separation in reaction centers and the further transfer of electrons along the electron transport chain are studied.

In addition to studying the mechanisms of reactions occurring with the participation of paramagnetic particles, the EPR method is widely used to study the structural and dynamic properties of macromolecules and biomembranes.

Recently, “paramagnetic probe”, “spin label” and “spin trap” methods are often used to study biological and polymer systems. All of them are based on the use of stable nitric acid radicals of various structures, or more precisely on the analysis of changes in the linewidth of EPR spectra caused by the rotational and translational diffusion of these radicals.

The main idea of ​​the spin label and probe method is to attach a free radical to a particular functional group of a protein and study the characteristics of its EPR signals. The most convenient in this regard are nitroxyl radicals containing a free radical group:

where R 1 and R 2 are different chemical groups.

Spin Mark Method consists in the fact that a stable radical is attached to a non-paramagnetic molecule by a covalent or some other bond so that the free valence is unaffected. The nature of the motion is clearly visible in the shape of the spectrum and serves as an important source of information about the parent molecule.

If a molecule is inserted into a protein molecule and held there by electrostatic forces or hydrophobic interactions, then such a molecule is called spin probe. The method is based on the study of the rotational and translational mobility of a radical probe in aqueous or organic media or in a polymer matrix. The mobility of a radical depends on the mobility of the molecules of the environment, so the radical is a kind of molecular sensor of structural and dynamic information about the local environment.

The shape of the EPR signal produced by a spin label or probe depends on the microenvironment of the nitroxide radical and, first of all, on the rotational mobility of the group it belongs to.

The main disadvantage of spin labels and probes is that although these molecules are small, when they are included in the lipid bilayer, they somewhat change its properties.

The basis of the method "spin traps" lies the reaction of a non-paramagnetic molecule (trap) specially introduced into the system under study with a short-lived radical, which results in the formation of a stable radical. The kinetic behavior of the resulting stable radical and its structure provide information about the kinetics and mechanism of processes in the system under study.

The objects of research in chemistry using EPR spectroscopy are: 1) free radicals in intermediate products of organic reactions; 2) reaction kinetics; 3) chemistry of surface phenomena; 4) destruction resulting from irradiation; 5) polymerization caused by free radicals; 6) free radicals frozen at low temperatures; 7) metals of variable valency and their complexes.

The EPR method provides a valuable contribution to the study of the kinetics and mechanisms of chemical reactions. First, measuring the linewidth in EPR spectra can be used to determine the rate constants of processes involving paramagnetic particles, the characteristic lifetime of which lies in the range of 10 -5 -10 -10 s. Secondly, the EPR method makes it possible to detect paramagnetic particles with high sensitivity under different conditions, which provides valuable information about reaction mechanisms. Thirdly, an EPR spectrometer can be used as an analytical instrument for detecting the concentration of reacting paramagnetic molecules during reactions. The number of paramagnetic centers in a sample is proportional to the area under the absorption spectrum.

The EPR method is widely used to study rapid processes associated with changes in the molecular structure of radicals. These processes include inhibited rotation and conformational transitions.

For short-lived radicals, the sensitivity of the method can be increased by using a flow system or continuous irradiation. ESR spectra of unstable radicals can be obtained by recording them in glasses, frozen noble gas matrices, or crystals.

Interview Questions

1. Theoretical foundations of the method.

2. Analytical parameters of the EPR spectrum.

3. EPR spectrometers.

4. Application of EPR.

Test tasks

1. Resonance condition in the EPR method:

a) n= gH 0 (1-s) / 2p; b) δ = (ΔН/Н 0); c)hn=gβH 0; d) δ = (Δν/ν 0)/(ΔН/Н 0).

2. What happens at the moment of resonance in the EPR method:

a) absorption of radiation quanta occurs, spin reorientation does not occur;

b) absorption of radiation quanta and reorientation of spins occurs, i.e. transition from a lower energy state to a higher one and vice versa. The number of transitions from bottom to top is greater than the number of transitions from top to bottom.

c) absorption of radiation quanta and reorientation of spins occurs, i.e. transition from a lower energy state to a higher one and vice versa. The number of transitions from top to bottom is greater than the number of transitions from bottom to top.

3. EPR spectra parameters:

a) g-factor, absorption band width, absorption line intensity;

b) total number of signals, signal intensity, chemical shift, signal multiplicity;

c) g-factor, absorption band width, absorption line intensity, HFS of EPR spectra.

MASS SPECROMETRY

This method is fundamentally different from spectroscopic methods. Mass spectrometry methods are based on the ionization of a substance, the separation of ions, according to the ratio ( m/z), and recording the mass of the resulting fragments.

The theoretical and experimental foundations of mass spectrometry were laid by D.D. Thomson, who for the first time in 1912 created a device for obtaining the mass spectrum of positive ions. However, his instrument had low resolution. His student F. Aston in 1918 significantly increased the resolution and discovered isotopes of elements for the first time using his instrument. Almost simultaneously with F. Aston in Chicago, A. Dempster designed the first mass spectrometer, in which a transverse magnetic field served as an analyzer, and ion currents were measured by electrical methods. Its circuit is also used in modern devices.

Ionization of molecules must be carried out under conditions under which the resulting ion, regardless of the ionization method, does not undergo any collisions with other molecules or ions. This is necessary to establish the relationship between the properties of the ion and the molecule.

Ionization methods

Ionization can be carried out using various methods.

1. Electron impact ionization (EI) method.

This is the most common method for producing ions due to the simplicity and availability of ion sources and their high efficiency. Let us assume that a flow of electrons passes through the vapors of the substance, the energy of which can be gradually increased. If this energy reaches a certain level, then when an electron collides with a molecule, an electron can be “knocked out” from it with the formation of a molecular ion:

polyatomic molecule molecular ion (radical cation)

The lowest energy of bombarding electrons at which an ion can be formed from a given molecule is called ionization energy of a substance. Ionization energy is a measure of the strength with which a molecule holds the least bound electron. For organic molecules, the ionization energy is 9 ÷ 12 eV.

If the electron energy significantly exceeds the ionization energy, then the resulting molecular ion receives excess energy, which may be sufficient to break the bonds in it. The molecular ion disintegrates into particles of smaller mass (fragments). This process is called fragmentation . In the practice of mass spectrometry, electrons with an energy of 30÷100 eV are used, which ensures fragmentation of the molecular ion.

Molecular ions- these are ions whose masses are equal to the mass of the ionized molecule. Unfortunately, there are no direct methods for determining the structure of ions. Therefore, the assumption of the identity of the structure of the molecular ion (M +) and the neutral molecule (M) is often used. The likelihood of forming a molecular ion is greater for simple, small molecules. As the number of atoms in a molecule increases, the probability of fragmentation of a molecular ion increases.

There are two main types of molecular ion fragmentation known: dissociation and rearrangement.

Dissociation- decay of a molecular ion while maintaining the sequence of bonds. As a result of the process, a cation and a radical are formed:

Dissociation of hydrocarbons results in fragments with odd m/z ratios.

Regrouping is accompanied by a change in the sequence of bonds, resulting in the formation of a new radical cation of smaller mass and a neutral stable molecule (H 2 O, CO, CO 2, etc.):

Rearrangement of hydrocarbons and oxygen-containing compounds leads to a fragment with an even m/z ratio. Measuring the mass of the resulting fragments and their relative quantity provides valuable information about the structure of organic compounds.

Let's consider the device of a mass spectrometer (Fig. 1). The mass spectrometer must contain components to perform the following functions: 1) ionization of the sample, 2) acceleration of ions by an electric field, 3) distribution of ions according to the m/z ratio, 4) detection of ions using a corresponding electrical signal.

Fig.1. Mass spectrometer device

1 - source of electrons; 2 - ionization chamber; 3 - accelerating plates (negative potential); 4 - magnet; 5 - slot;

6 - ion collector (ion detector)

To obtain a mass spectrum, vapors of substances are introduced into the ionization chamber in small quantities using a special injection system. (2) , where a deep vacuum is maintained (pressure 10 -6 mm Hg). Molecules of a substance are bombarded by a stream of electrons emitted by a hot cathode (1). The resulting ions are pushed out of the ionization chamber by a small potential difference (3). The resulting stream of ions is accelerated, focused by a strong electric field and caught in a magnetic field (4).

As a result of the bombardment of substance molecules by electrons, particles with a positive or negative charge, as well as neutral particles, are formed. When a stream of particles passes through a magnetic field, neutral particles do not change direction, but positive and negative particles are deflected in different directions. The amount of deflection of ions is proportional to their charge and inversely proportional to their mass.

Each individual ion, characterized by a specific m/z value, moves along its own trajectory at a given magnetic field strength. The mass scanning interval can be changed by varying either the magnetic field strength or the electric field potential.

In conventional mass spectrometry, it is customary to register only particles that have a positive charge, because When molecules are bombarded with electrons, there are usually more positively charged ions than negatively charged ones. If negatively charged ions also need to be studied, the sign of the acceleration potential (accelerator plates) should be changed.

If a recording device is installed at the exit of ions from a magnetic field, then particles with different m/z values ​​will give separate signals. The intensity of the signals will be proportional to the number of particles with a given m/z value. The intensity of the signals is defined as their height, expressed in mm. The height of the peak with the maximum intensity is taken as 100% (base peak), the intensity of the remaining peaks is recalculated proportionally and expressed as a percentage.

As the m/z ratio increases, the difference in the deflection by the magnetic field of particles that differ by one atomic mass unit decreases. In this regard, an important characteristic of mass spectrometers is their resolution (R) , which determines the maximum mass of ions that differ by one atomic mass unit (for which the instrument separates the peaks by at least 90%):

where M is the maximum mass for which the peak overlap is less than 10%; ΔM is one atomic mass unit.

Standard devices have R ≈ 5000/1, and for devices with double focusing of ion flow R ≈ 10000/1 and even more. Such devices are capable of detecting differences in the molecular mass of ions up to 0.0001. A dual focusing mass spectrometer can easily separate peaks from ions with the same nominal molecular weights but different elemental compositions. For example, it can distinguish between N2 (28.0061), CO (27.9949), and C2H4 (28.0313).

Establishing an empirical formula from mass spectral data is not a simple task, but it can be solved using a suitable algorithm. To obtain a mass spectrum, a negligible amount of the substance is required - about 1 μg.

2. Chemical ionization (CI).

In this method, the sample is diluted with a large excess of “reagent gas” before irradiation with an electron beam. The probability of primary ionizing collisions between electrons and sample molecules is then so small that primary ions are formed almost exclusively from reactant molecules. Gases with low molecular weight are usually used as reagents, for example, CH 4, iso-C 4 H 10, NH 3 and inert gases (Ar, He). Secondary ions are formed by the transfer of a hydrogen atom or electron.

If methane is the reagent gas, then the reactions proceed in the following sequence:

CH 4 + ē → CH 4 + + 2ē

CH 4 + + ē → CH 3 + +H + + 2ē

CH 4 + + CH 4 → CH 5 + + CH 3

CH 3 + + CH 4 → C 2 H 5 + +H2

R-CH 3 + CH 5 + → R-CH 4 + + CH 4

where R-CH 3 is a molecule of the substance under study.

Research has shown that CH 5 particles + and C2H5 + together make up about 90% of the ions present in this system. Mass spectra obtained after chemical ionization are much simpler, contain fewer peaks, and are therefore often easier to interpret.

Electron paramagnetic resonance (EPR) is the phenomenon of resonant absorption of electromagnetic radiation by a paramagnetic substance placed in a constant magnetic field. Caused by quantum transitions between magnetic sublevels of paramagnetic atoms and ions (Zeeman effect). EPR spectra are observed mainly in the ultrahigh frequency (microwave) range.

The electron paramagnetic resonance method makes it possible to evaluate the effects that appear in EPR spectra due to the presence of local magnetic fields. In turn, local magnetic fields reflect the picture of magnetic interactions in the system under study. Thus, the EPR spectroscopy method allows one to study both the structure of paramagnetic particles and the interaction of paramagnetic particles with the environment.

The EPR spectrometer is designed for recording spectra and measuring the parameters of the spectra of samples of paramagnetic substances in the liquid, solid or powder phase. It is used in the implementation of existing and development of new methods for studying substances using the EPR method in various fields of science, technology and healthcare: for example, to study the functional characteristics of biological fluids based on the spectra of spin probes introduced into them in medicine; to detect radicals and determine their concentration; in the study of intramolecular mobility in materials; in agriculture; in geology.

The basic device of the analyzer is a spectrometric unit - an electron paramagnetic resonance spectrometer (EPR spectrometer).

The analyzer provides the ability to study samples:

• with temperature regulators - sample temperature control systems (including in the temperature range from -188 to +50 ºС and at liquid nitrogen temperature);
• in cuvettes, ampoules, capillaries and tubes using automatic sample changing and dosing systems.

Features of the EPR spectrometer

A paramagnetic sample in a special cell (ampoule or capillary) is placed inside a working resonator located between the poles of the spectrometer electromagnet. Electromagnetic microwave radiation of constant frequency enters the resonator. The resonance condition is achieved by linearly changing the magnetic field strength. To increase the sensitivity and resolution of the analyzer, high-frequency magnetic field modulation is used.

When the magnetic field induction reaches a value characteristic of a given sample, resonant absorption of the energy of these vibrations occurs. The converted radiation then enters the detector. After detection, the signal is processed and sent to a recording device. High-frequency modulation and phase-sensitive detection convert the EPR signal into the first derivative of the absorption curve, in the form of which electron paramagnetic resonance spectra are recorded. Under these conditions, the integral EPR absorption line is also recorded. An example of the recorded resonant absorption spectrum is shown in the figure below.

ELECTRONIC PARAMAGNETIC RESONANCE(EPR) - resonant absorption (radiation) el-magnetic. 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 paramagnetic. resonance and a more general phenomenon - magnetic resonance. It is the basis of radio spectroscopic methods for studying substances (see Radiospectroscopy). It has a synonym - electron spin resonance (ESR), emphasizing the important role in the phenomenon of electron spins. Opened in 1944 by E. K. Zavoisky (USSR). As a paramagnetic particles (in the case of condensed matter-paramagnetic centers) that determine paramagnetism can be electrons, atoms, molecules, complex compounds, crystal defects, if they have a non-zero magnetic moment. The source of the magnetic moment can be the unpaired spin or the nonzero total spin (momentum of the number of motions) of electrons.

In permanent magnet. fields as a result of removing degeneracy in paramagnetic fields. particles a magnetic system arises. (spin) sublevels (see Zeeman effect). Between them under the influence of electric magnet. radiation, transitions occur leading to the absorption (emission) of a photon with frequency w ij = ||/.In the case of one electron in a permanent magnet. field H energies of sublevels = bg b H/ 2 and, accordingly, the ESR frequency w is determined by the relation

where g is the spectroscopic factor. splitting; b - Bohr magneton; usually, H= 10 3 5-10 4 E; g2.

Experimental methods. EPR spectrometers (radio spectrometers) operate in the centimeter and millimeter wavelength ranges. Microwave technology is used - a generator (usually klystron), a system of waveguides and resonators with a detecting device. A sample volume of several. mm 3 is placed in the resonator area, where the electromagnetic component. The wave (usually magnetic) causing the transitions has an antinode. The resonator is installed between the poles of an electromagnet - a source of permanent magnet. fields. A resonant condition of type (1) is usually achieved by changing the field strength H at a fixed generator frequency w. Magnet value fields at resonance ( H p) in general depends on the orientation of the vector H in relation to the sample. The absorption signal in the form of a typical bell-shaped burst or its derivative (Fig. 1) is observed using an oscilloscope or recorder. Naib. The absorption signal proportional to the imaginary part of the dynamic magnetic field is often studied. susceptibility (c"") of the sample. However, in a number of cases, its real part (c") is recorded, which determines the fraction of magnetization that varies in phase with the magnetic component of the electromagnetic wave. ESR can manifest itself in the form of microwave analogues of the optical Faraday and Cotton-Mouton effects. For their registration, 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 have become widespread, making it possible to analyze the time dependences of EPR signals (the so-called spin induction and spin echo). There are a number of other techniques for studying relaxation. processes, in particular for measuring relaxation times.

Rice. 1. Electron paramagnetic resonance: A - paramagnetic particle with spin S= 1/2, placedexposed to an external magnetic field, has two sublevels (and ), each of which changes the propulsionnationally H and depends on its orientation along relative to the crystallographic axes, specifymy angles q and f. At resonant values, the magnetno field H p1 and H p2 (angles q 1, (j 1 and q 2, j 2) difference becomes equal to the microwave energy quantum-radiation. Moreover, in the absorption spectrum ( b)observecharacteristic bursts are given near N r 1 and Hp 2 (withthe absorption signal and its derivative are given).

Theoretical description. To describe the EPR spectrum it is used spin Hamiltonian, which has its own form for each specific case. In general, it can be presented in a form that takes into account all possible paramagnetic interactions. particles (center):

where describes the interaction with external. mag. field H ; - interaction with intracrystalline electric field; - with mag. moment of its own and surrounding nuclei ( hyperfine interaction and super-ultrafine interaction); - spin-spin interactions paramagnetic centers among themselves (exchange interaction, dipole-dipole, etc.); -interaction with the attached external pressure P(deformations); -with ext. electric field E . Each term included in (2) can consist of several. terms, the type of which depends on the magnitude of the electron and nuclear spins and the local symmetry of the center. Frequently occurring expressions are of the form;

Where g, a, A, J, C, R- parameters of the theory, S (i) And I (k) - i th and k-th spin of electrons and nucleus; -unit matrix. The spin Hamiltonian (2) is usually referred to as one electron or electron-oscillation. term (usually the main one), assuming that other terms are separated from it by an amount significantly exceeding the energy of the EPR transition quantum. But in some cases, for example. in the presence of Jahn-Teller effect, excited terms can be quite close and must be taken into account when describing EPR spectra. Then, to preserve the formalism of the spin Hamiltonian, one can introduce eff. spin( S ef), associated with the total number of states of all levels ( r) ratio 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 for 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 causing and relaxation. processes. Energy the structure and wave functions are found by solving the system of equations corresponding to (2). The number of levels is equal

Where n And p-the number of spins of electrons and nuclei appearing in (2). Usually S And I take values ​​from 1/2 to 7/2 ; n= 1, 2; p= l-50, which indicates the possibility of the existence of secular equations of a high order. To overcome technical Difficulties in diagonalization (2) use approximate (analytical) calculations. Not all terms (2) are the same in size. Usually they are superior to other members, and also significantly less than the previous ones. This makes it possible to develop perturbation theory in several ways. stages. In addition, special computer programs.

The goal is phenomenological. theory - finding for definition. transition expression for H p in the function of the spin Hamiltonian parameters and angles characterizing the orientation of the external. fields relative to crystallographic. axes. By comparison ( H p) theory with ( H p) exp, the correctness of choice (2) is established and the parameters of the spin Hamiltonian are found.

The parameters of the spin Hamiltonian are calculated independently using quantum mechanics methods, based on the definition. paramagnetic models center. In this case, the crystalline theory is used. fields, molecular orbital method, other methods quantum chemistry and solid state theory. Basic The difficulty of this problem lies in determining the electron energy. structures and wave functions paramagnetic. 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 entire complex of problems, few complete calculations of the parameters of the spin Hamiltonian have been carried out so far, and not all of them have achieved satisfactory agreement with experiment. Usually one is limited to estimates in the order of magnitude, using approximate values.

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. Thus, in the presence of only Zeeman interaction, the expression for energy has the form = g b H + M, Where M- quantum number of the operator, taking 2 S+1 values: - S, - S+ 1, .... S-1, S. Magn. el-magnetic component waves in this case causes only transitions with the selection rules DM = b 1, and, due to the equidistance of the levels, one line will be observed in the EPR spectrum. Violation of equidistance occurs due to other terms of the spin Hamiltonian. Thus, the axially symmetric term of , characterized by the parameter D, adds to member , H p turns out to depend on M, and 2 will be observed in the spectrum S lines. Accounting for the term AS z I z of leads to addition (D ) st = AMt, Where T- 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= b2), which increases the number of lines in the spectrum.

Specific splitting of lines occurs under the influence of electricity. fields (term). In crystals (corundum, wolframites, silicon) there are often inversion nonequivalent positions, in which impurity ions can be found with equal probability. Since mag. 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 two groups of lines will manifest itself in the form of splitting.

In the absence of magnetic field ( =0), the splitting of levels, called initial, is due to other terms (2). The number of levels that arise and the multiplicity of their degeneracy depend on the magnitude of the spin and the symmetry of the paramagnetic. center. Transitions are possible between them (the corresponding phenomenon is called field-free resonance). To implement it, you can change the frequency v el-magn. radiation, or v= const change the distance between external levels. electric field, pressure, temperature change.

Determination of the symmetry of a paramagnetic center. Angle addiction H p (q, f) reflects the symmetry of the spin Hamiltonian, which in turn is associated with the symmetry of the paramagnetic. center. This makes it possible by type of function H p (q, f), found experimentally, determine the symmetry of the center. In the case of highly symmetric groups ( O h , T d , C 4u, etc.) function H p (q, f) has a number of characteristic features: 1) the positions of the extrema for lines of different transitions coincide; 2) the distance between the extrema is p/2 (orthogonality effect); 3) function H p is symmetric with respect to the positions of extrema, etc. In the case of low-symmetric groups ( C 1 , C 2 , C 3, etc.) all these patterns are violated (low symmetry effects). These effects are used to determine the structure of defects.

The usual EPR corresponds to the spin Hamiltonian, which does not take into account the electric energy. fields (=0). It includes only the operators of the moment of the quantity of motion and the magnetic field. 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 the determination of paramagnetic symmetry. centers, which can be eliminated using external. electric field. Linear by E the operator is different for different point groups that do not have an inversion center (for inversion centers = 0). At the 1st stage of experiments without a field E a set of groups with the same Hamiltonian is determined, corresponding to the symmetry of the spectrum of ordinary EPR. At the 2nd stage, the field is used E and the fact that each set of groups includes only one group with the center of inversion is taken into account.

Study of disordered systems. Along with the study of paramagnetic centers in perfect EPR crystals are also used to study disordered systems(powders, glasses, solutions, crystals with defects). A feature of such systems is the unevenness (heterogeneity) of conditions in the locations of the centers due to differences in internal. electric (magn.) fields and deformations caused by structural distortions of the crystal; non-equivalence of paramagnetic orientation. centers in relation to external fields; heterogeneity of the latter. This leads to a scatter in the parameters of the spin Hamiltonian and, as a consequence, to an inhomogeneous broadening of the EPR lines. Studying these lines allows one to obtain information about the nature and degree of defects in the crystal. Inhomogeneous broadening of any nature can be considered from a single point of view. The general expression for the line shape is:

where y is a function that describes the initial shape of the line without taking into account disturbing factors; V (F)- transition probability per unit time; r( F) - parameter distribution function F(F 1 , F 2 , .·., F k), characterizing the mechanisms of broadening (components of fields, deformations, angles). So, in the case of chaotically oriented paramagnetic centers (powders) under F it is necessary to understand the Euler angles, which characterize the orientation of the powder particle relative to the coordinate system associated with the external fields. In Fig. Figure 2 shows a typical EPR spectrum of a powder for a spin Hamiltonian of the form Instead of corner dependence of a single narrow line inherent in paramagnetic centers in single crystals, in this case an orientationally broadened envelope line appears.

Rice. 2. Electron paramagnetic resonance signalsa chaotically oriented paramagnetic centers. Absorption line ( A) and its derivative ( b ) in the case of rhombic symmetry of the spin HamiltonNiana. The characteristic points of the spectrum are related to the parameters of the spin Hamiltonian by the relation Hpi=w/bg iii .

Relaxation processes. EPR is accompanied by processes of restoration of the damaged electromagnetic field. radiation of equilibrium in a medium corresponding to the Boltzmann distribution. These are relaxing. processes are caused by the connection between paramagnetic. center and lattice, as well as centers between the collection. Accordingly, they distinguish between s and n-spin relaxations. If transitions under the influence of electromagnetic waves predominate, a saturation phenomenon occurs (equalization of level populations), manifested in a decrease in the EPR signal. Relaxation. processes are characterized by relaxation times and are described by kinetics. ur-niyami (see Basic kinetic equation). In case of two levels i And j level for populations n i And n j- look like

Where a = u 0 ij + u ij , b = u 0 ji + u ji, u 0 ij and u ij-probability of transition per unit time from level i per level j under the influence of electromagnetic waves and relaxation mechanisms respectively ( u 0 ij = u 0 ji). Relaxation time T p is determined by the expression T p = (u ij+u ji) -1 and characterizes the rate at which equilibrium is established. Relaxation. 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, which manifests itself in the same way in all paramagnetic waves. centers is usually called homogeneous. It determines, in particular, the function y included in (3).

Double resonances. To describe the spin system, the concept of spin temperature is introduced T s. The relationship between the population of levels and temperature that determines the Boltzmann distribution is generalized to the case of nonequilibrium populations. From it, for arbitrary population ratios, the top. ( p in) and lower ( n n) levels it follows that Т s =-()/ln( n V / n n). At n in = n n (saturation) T s =, and when n in > n n value T s< 0. The possibility of creating a non-equilibrium population and, in particular, situations in which T s = 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, A); obtaining a source of el-magn. radiation by creating a higher population at the upper level than at the lower level (Fig. 3, b). The principle of signal amplification forms the basis for the implementation of a number of double resonances in cases where the system contains spins of different types. Thus, in the presence of electron and nuclear spins, double electron-nuclear resonance (ENDR) is possible. Hyperfine level splitting is usually much less than the Zeeman splitting. This creates the opportunity to enhance transitions between hyperfine sublevels by saturating spin-electron transitions. In the ENDOR method, not only the sensitivity of the equipment increases, 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 difficult due to for overlapping lines). Thanks 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 kernels of many coordinations. spheres near the defect, which makes it possible to unambiguously determine its nature and properties. Double resonances associated with the production of el-magnetic sources. radiation formed the basis for the operation of quantum generators, which led to the creation and development of a new direction - quantum electronics.

Rice. 3. Double resonance in a multilevel system. There are 3 levels, for which n 1 0 - n 0 2 >>p 0 2 - P 0 3 (P 0 - equilibrium value); A- gain absorption; Levels 1 and 2 are saturated with intense electromagnetic radiation, so 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 frequency v 32 increases sharply; b-maser effect; saturation of drive levels 1 and 3goes to the necessary condition [ n 3 -n 2 (n 0 1 -n 0 2)/2>0] for generating el-magn. radiation at frequency v 32 ·

Conclusion. EPR has found wide application in various fields. fields of physics, chemistry, geology, biology, medicine. Intensively used to study the surface of solids, phase transitions, and disordered systems. In semiconductor physics, EPR is used to study shallow and deep point impurity centers, free charge carriers, carrier-impurity pairs and complexes, radiation. defects, dislocations, structural defects, amorphization defects, interlayer formations (such as Si - SiO 2 boundaries), carrier-impurity interaction, recombination processes, photoconductivity and other phenomena are studied.

Lit.: Altshuler S. A., Kozyrev B. M., Electron paramagnetic resonance of compounds of intermediate group elements, 2 ed., M., 1972; Poole Ch., Technique of EPR spectroscopy, trans. from English, M., 1970; Abraham A., Bleaney B., Electron paramagnetic resonance of transition ions, trans. from English, g. 1-2, M., 1972-73; Meilman M. L., Samoilovich M. I., Introduction to EPR spectroscopy of activated single crystals, M., 1977; Electrical effects in radio spectroscopy, ed. M. F. Daygena, M., 1981; Roytsin A. B., Mayevsky V. N., Radio spectroscopy of the surface of solid bodies, K., 1992; Radiospectroscopy of solids, ed. A. B. Roytsina, K., 1992. A. B. Roitsin.

The phenomenon of electron paramagnetic resonance

If a paramagnetic atom is placed in a magnetic field, then each of its energy levels will be split into a number of sublevels equal to $2J+1$ (the number of possible $m_J)$. The interval between adjacent levels is equal to:

In the event that an atom in this state is placed in an electromagnetic wave having a frequency $\omega $, which satisfies the condition:

then, under the influence of the magnetic component of the wave, in accordance with the selection rule, atomic transitions will occur between neighboring sublevels, within one level. This phenomenon is called electron paramagnetic resonance (EPR). It was first noted by E.K. Zavoisky in 1944. Since ESR is associated with resonance, transitions appear only at a certain frequency of the incident wave. This frequency can be easily estimated using expression (2):

At $g\approx 1$ and typical magnetic field induction, which is used in laboratory conditions, $B\approx 1\ T$, $\nu =(10)^(10)Hz$ is obtained. Which means that the frequencies are localized in the radio range (microwave).

During the phenomenon of resonance, energy is transferred from the field to the atom. In addition, when an atom moves from high Zeeman sublevels to lower sublevels, energy is transferred from the atom to the field. It should be noted that in the case of thermal equilibrium, the number of atoms with lower energy is greater than the number of atoms with higher energy. This means that transitions that increase the energy of atoms prevail over transitions to the side with lower energy. It turns out that the paramagnetic absorbs the energy of the field in the radio range and at the same time increases its temperature.

Experiments with the phenomenon of electron paramagnetic resonance made it possible, using expression (2), to find one of the parameters: $g,B\ or\ (\omega )_(rez)$ from the remaining quantities. Thus, by measuring $B$ and $(\omega )_(rez)$ with high accuracy in the resonance state, the value of the Lande factor and the magnetic moment of the atom in the state with J are found.

In liquids and solids, atoms cannot be considered isolated. Their interaction cannot be ignored. This leads to the fact that the intervals between neighboring sublevels during Zeeman splitting are different, and the EPR lines have a finite width.

EPR

So, the phenomenon of electron paramagnetic resonance consists in the absorption of microwave radio emission by a paramagnet due to transitions between sublevels of Zeeman splitting. In this case, the splitting of energy levels is caused by the influence of a constant magnetic field on the magnetic moments of the atoms of the substance. The magnetic moments of atoms in such a field are oriented along the field. Simultaneously with this, the Zeeman energy levels are splitting and redistributed among these atomic levels. The occupancy of sublevels by atoms turns out to be different.

In a state of thermodynamic equilibrium, the average number of atoms ($\left\langle N\right\rangle $) occupying a given sublevel can be calculated using the Boltzmann formula:

where $\triangle E_(mag)\sim mH$. Sublevels with a lower magnetic quantum number ($m$) have more atoms, as states with lower potential energy. This means that there is a preferential orientation of the magnetic moments of atoms along the magnetic field, which corresponds to the magnetized state of the paramagnet. When an alternating magnetic field with a frequency equal to (a multiple of) the transition frequency between sublevels of Zeeman splitting is applied to a paramagnet, resonant absorption of electromagnetic waves occurs. It is caused by an excess of the number of transitions, which are associated with an increase in the magnetic quantum number by one:

over the number of transitions like:

Thus, due to the resonant absorption of the energy of an alternating magnetic field, atoms will make transitions from lower, more filled levels to upper levels. Absorption is proportional to the number of absorbing atoms per unit volume.

If a substance is composed of atoms with one valence electron in the s state, having a total magnetic moment equal to the spin magnetic moment of the s electron, then EPR is most effective.

A special paramagnetic resonance is the resonant absorption of electromagnetic waves by conduction electrons in metals. It is associated with the spin of electrons and the spin paramagnetism of the electron gas in such a substance. In ferromagnets, ferromagnetic resonance is distinguished, which is associated with the reorientation of electronic moments in domains or between them.

Radio spectroscopes are used to study electron paramagnetic resonance. In such devices, the frequency ($\omega $) remains unchanged. Change the induction of the magnetic field (B), which creates an electromagnet (Fig. 1).

Figure 1. Electron paramagnetic resonance (EPR). Author24 - online exchange of student works

A small sample A is placed in a cavity resonator R, which is tuned to a wavelength of about 3 cm. Radio waves of this length are created by a generator G. These waves are fed through a waveguide V to the resonator. Some of the waves are absorbed by sample A, some of them enter detector D through the waveguide. During the experiment, a smooth change in the magnetic field induction (B), which is created by an electromagnet, is carried out. When the induction value satisfies the condition for the occurrence of resonance (2), the sample begins to intensively absorb the wave.

Note 1

EPR is one of the simplest radiospectroscopy methods.

Examples

Example 1

Exercise: What is the magnetic moment of the $Ni$ atom in the $(()^3F)_4$ state if resonant energy absorption occurs under the influence of a constant field with magnetic induction $B_0$ and an alternating magnetic field with induction $B_0$ perpendicular to the constant field. The frequency of the alternating field is $\nu $.

Solution:

As is known, in the state of resonance the following equality holds:

\[\hbar \omega =h\nu =\delta E=(\mu )_bgB\left(1.1\right).\]

From formula (1.1) we find the Lande factor:

For a given state ($(()^3F)_4$) we have: $L=3$, $S=1$, $J=4$. The magnetic moment is given using the expression:

\[\mu =(\mu )_bg\sqrt(J(J+1))=\frac(h\nu )(B_0,\ )\sqrt(20).\]

Answer: $\mu =\frac(h\nu )(B_0,\ )\sqrt(20).$

Example 2

Exercise: What useful information can be obtained from studying electron paramagnetic resonance?

Solution:

Having empirically obtained resonance from resonance conditions, one can find one of the quantities: Lande factor ($g$), magnetic field induction under conditions of resonant absorption of energy by an atom (B), resonant frequency ($(\omega )_(rez)$). In this case, B and $(\omega )_(rez)$ can be measured with high accuracy. Consequently, EPR makes it possible to obtain the value of $g\ $ with high accuracy and, consequently, the magnetic moment of the atom for a state with quantum number $J$. The value of the quantum number S is determined by the multiplicity of the spectra. If $g,\ J,\ S$ are known, it is easy to calculate $L$. It turns out that all the quantum numbers of the atom and the spin orbital and total magnetic moments of the atom become known.

The electron paramagnetic resonance method is the main method for studying paramagnetic particles. Paramagnetic particles of important biological significance include two main types: free radicals and complexes of metals of variable valency (such as Fe, Cu, Co, Ni, Mn).

The method of electron paramagnetic resonance was discovered in 1944 by E.K. Zavoisky while studying the interaction of electromagnetic radiation in the microwave range with metal salts.

The EPR method is based on the absorption of electromagnetic radiation in the radio range by unpaired electrons located in a magnetic field.

The EPR method allows us to study the properties of paramagnetic centers by recording the absorption spectra of electromagnetic radiation by these particles. Knowing the characteristics of the spectra, one can judge the properties of paramagnetic particles.

The main characteristics of the spectra include amplitude, linewidth, g-factor and hyperfine structure of the spectra.

Application of spin tags

Spin labels are chemically stable paramagnetic molecules that are used as molecular probes to study the structure and molecular mobility of various physicochemical and biological systems. The essence of the spin label method is as follows. Paramagnetic molecules are introduced into the system under study as spin probes, which produce characteristic electron paramagnetic resonance (EPR) signals. The EPR signals of spin labels depend on their molecular mobility and the physicochemical properties of the immediate environment. Therefore, by observing the EPR signals of molecular probes, it is possible to study the structural characteristics of the system under study and the dynamics of the molecular processes occurring in it. The term “spin marks” comes from the English word “spin” (spindle, top), which refers to the intrinsic mechanical momentum of an electron. An electron, as is known from quantum mechanics, has a mechanical moment equal to the value "/2, and its own magnetic moment, where " is Planck's constant, e and m are the charge and mass of the electron, c is the speed of light. The paramagnetic properties of molecular probes are determined by the presence of an unpaired electron in them, which has spin and is the source of the EPR signal. Stable nitroxyl radicals are usually used as spin labels. All molecules of spin labels, despite the diversity of their chemical structure, as a rule, contain the same paramagnetic fragment - a chemically stable nitroxyl radical (>N-OJ). An unpaired electron is localized on this radical, serving as a source of the ESR signal. The specific choice of spin labels is determined by the research problem. For example, in order to monitor conformational rearrangements of proteins using spin labels, label molecules are usually “sewn” to certain regions of the protein. In this case, the spin label must contain a special reaction group that can form a covalent chemical bond with the amino acid residues of the protein molecule. To study the properties of artificial and biological membranes, fat-soluble spin labels are usually used that can be incorporated into the lipid layer of the membrane.

The phenomenon of electron paramagnetic resonance (EPR) is 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. EPR is also called 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 in:

• * atoms and molecules that have an odd number of electrons in their orbitals - H, N, NO2, etc.;
• * chemical elements in different 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-, O2-, CO2-, CO23-, CO3-, CO33- and many others;
• * molecules with an even number of electrons, the paramagnetism of which is due to quantum phenomena of the distribution of electrons in molecular orbitals - O2;
• * superparamagnetic nanoparticles formed during dissolution or in alloys with a collective magnetic moment that behave like an electron gas.

Structure and properties of EPR spectra

The behavior of magnetic moments in a magnetic field depends on various interactions of unpaired electrons, both among themselves and with their immediate environment. The most important of them are spin-spin and spin-orbit interactions, interactions between unpaired electrons and the nuclei on which they are localized (hyperfine interactions), interactions with the electrostatic potential created by ions in the immediate environment at the location of unpaired electrons, and others. Most of the listed interactions lead to a natural splitting of lines. In the general case, the EPR spectrum of a paramagnetic center is multicomponent. An idea of ​​the hierarchy of basic splittings can be obtained from the following diagram (definitions of the notation used are given below):

The main characteristics of the EPR spectrum of a paramagnetic center (PC) are:

• * number of lines in the EPR spectrum of a particular PC and their relative intensities.
• * Fine structure (TS). The number of TC lines is determined by the spin value S of the PC and the local symmetry of the electrostatic field of the immediate environment, and the relative integral intensities are determined by the quantum number mS (the magnitude of the projection of the spin onto the direction of the magnetic field). In crystals, the distance between the TC lines depends on the magnitude of the crystal field potential and its symmetry.
• * Ultrafine structure (HFS). HFS lines from a particular isotope have approximately the same integral intensity and are practically equidistant. If the PC core has several isotopes, then each isotope produces 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 different PC isotopes 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.
• * Super ultrafine structure (USHS). The number of CCTS 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 Il = 1/2 obeys the law of binomial distribution with the exponent nl. The distance between the SCHS 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 special feature of EPR spectra is the form in which they are recorded. For many reasons, the EPR spectrum is recorded not in the form of absorption lines, but as a derivative of these lines. Therefore, in EPR spectroscopy, a slightly different terminology, different from the generally accepted one, is adopted to designate line parameters.

EPR absorption line and its first derivative: 1- Gaussian shape; 2- Lorentzian form.

• * The true line is a d-function, but taking into account relaxation processes it has a Lorentz form;
• * Line - reflects the probability of the process of resonant absorption of electromagnetic radiation from the PC and is determined by the processes in which spins participate;
• * Line shape - reflects the law of probability distribution of resonant transitions. Since, to a first approximation, deviations from resonant conditions are random, the shape of lines in magnetically diluted matrices has a Gaussian shape. The presence of additional exchange spin-spin interactions leads to a Lorentzian line shape. In general, the shape of a line is described by a mixed law;
• * Line width - DVmax - corresponds to the distance across the field between the extrema on the curved line;
• * Line amplitude - Imax - corresponds on the signal amplitude scale to the distance between extrema on the curved line;
• * Intensity - I0 - the probability value at the MAX point on the absorption curve, calculated by integrating 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 - B0 - corresponds to the intersection of the contour of the derivative dI/dB with the zero line (trend line);
• * position of EPR lines in the spectrum.

According to the expression hн = gвB, which determines the conditions of resonant absorption for PCs with spin S = 1/2, the position of the electron paramagnetic resonance line can be characterized by the value of the g-factor (analogue of the Lande spectroscopic splitting factor). The value of the g-factor is defined as the ratio of the frequency n at which the spectrum was measured to the value of magnetic induction B0 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 single 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 n, and the magnetic field B can vary within wide limits. There are some rather narrow microwave frequency ranges in which spectrometers operate.