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 the 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 the atom in this state is placed in an electromagnetic wave having a frequency of $\omega $, which satisfies the condition:
then under the influence of the magnetic component of the wave, in accordance with the selection rule, transitions of the atom between neighboring sublevels, within one level, will occur. This phenomenon is called electron paramagnetic resonance (EPR). E.K. was the first to note him. Zavoisky in 1944. Since EPR is associated with resonance, transitions appear only at a certain frequency of the incident wave. This frequency can be easily estimated using expression (2):
With $g\approx 1$ and a typical magnetic field induction used in a laboratory, $B\approx 1\ T$, $\nu =(10)^(10)Hz$ is obtained. Which means that the frequencies are localized in the radio range (UHF).
When resonance occurs, energy is transferred from the field to the atom. In addition, when an atom passes 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 paramagnet 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 rest of the quantities. Thus, by measuring $B$ and $(\omega )_(rez)$ with high accuracy in the state of resonance, one finds the Lande factor and the magnetic moment of the atom in the state with J.
In liquids and solids, atoms cannot be considered isolated. Their interaction cannot be neglected. It leads to the fact that the intervals between adjacent sublevels in Zeeman splitting are different, 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 the Zeeman splitting. In this case, the splitting of the energy levels is caused by the action 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, there is a splitting of the Zeeman energy levels and redistribution according to the given levels of atoms. The occupancy of sublevels by atoms turns out to be different.
In the state of thermodynamic equilibrium, the average number of atoms ($\left\langle N\right\rangle $) inhabiting a given sublevel can be calculated using the Boltzmann formula:
where $\triangle E_(mag)\sim mH$. Sublevels with a smaller magnetic quantum number ($m$) have more atoms as states with a smaller potential energy. This means that there is a predominant 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 is applied to a paramagnet with a frequency equal to (a multiple of) the frequency of the transition between the Zeeman splitting sublevels, resonant absorption occurs electromagnetic waves. 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 number of transitions like:
So, due to the resonant absorption of the energy of an alternating magnetic field, the atoms will make transitions from the lower, more filled levels, to the upper levels. Absorption is proportional to the number of absorbing atoms per unit volume.
If the substance is composed of atoms with one valence electron in state s, having a total magnetic moment equal to the spin magnetic moment of the s-electron, then EPR is most effective.
Resonant absorption of electromagnetic waves by conduction electrons in metals is considered a special paramagnetic resonance. It is related to the spin of electrons and the spin paramagnetism of the electron gas in such a substance. In ferromagnets, ferromagnetic resonance is isolated, which is associated with the reorientation of electronic moments in domains or between them.
Radiospectroscopes 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 papers
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 wavelength are generated 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) is carried out, which is created by an electromagnet. When the magnitude of the induction satisfies the resonance occurrence condition (2), the sample begins to absorb the wave intensively.
Remark 1
EPR is one of the most simple methods radiospectroscopy.
Examples
Example 1
Exercise: What is the magnetic moment of the $Ni$ atom in the $(()^3F)_4$ state if resonant absorption of energy 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 variable field is $\nu$.
Solution:
As is known, in the state of resonance the equality is fulfilled:
\[\hbar \omega =h\nu =\delta E=(\mu )_bgB\left(1.1\right).\]
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 by 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 the study of electron paramagnetic resonance?
Solution:
Having empirically obtained resonance from the resonance conditions, one of the quantities can be found: the Lande factor ($g$), the magnetic field induction under conditions of resonant absorption of energy by an atom (B), the resonant frequency ($(\omega )_(rez)$). Moreover, B and $(\omega )_(rez)$ can be measured with high accuracy. Consequently, the 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 from 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.
COURSE WORK
Abstract topic
"Application of the method of electron paramagnetic resonance in the study of oil and dispersed organic matter"
Introduction
Equipment
EPR spectrum parameters
Hyperfine structure (HFS) of EPR spectra
Factors affecting the feasibility of using the EPR method
Application of the EPR method
Determination of the Genesis of Dispersed Organic Matter and Oils
Conclusion
Bibliography
Introduction
I chose the topic "Application of the method of electron paramagnetic resonance in the study of oil and diffuse organic matter", since this topic is, firstly, very interesting, and secondly, relevant in modern science. The relevance of this topic is confirmed, in my opinion, by the fact that science is developing and humanity needs new methods for analyzing substances, more convenient and accurate.
Discovered in 1944 by the Soviet scientist E.K. Zavoisky, paramagnetic resonance developed into a large branch of physics - magnetic resonance radioscopy, which studies the properties of matter at the atomic and molecular level.
The most important qualities of the EPR method, as a method for the analysis of organic matter and oil, are:
Rapid analysis
Analysis Accuracy
Ease of detection of vanadium ions, which helps us to judge the genesis of this organic matter
The EPR method is of great importance for geochemistry and is widely used for the analysis of organic matter and oil.
The physical essence of the EPR method
The method of electron magnetic resonance (hereinafter referred to as EPR) was discovered by the Soviet physicist E.K. Zavoisky (1944, Kazan University), and became one of the main structural methods in physics, chemistry, biology and mineralogy. The EPR method is based on the phenomenon of electron paramagnetic resonance. This method is based on the absorption of electromagnetic waves by paramagnetic substances in a constant magnetic field. The energy absorption is recorded by a special radio spectrometer in the form of an EPR spectrum. The method allows obtaining information about the magnetic properties of a substance, which directly depend on its molecular structure. Using the EPR method, one can learn information about the structure of a substance; it is also promising in the study of the fine structure of organic matter, indicating the presence of free radicals of the aromatic type. EPR - spectroscopy is used not only in geochemistry, but also in a number of other sciences, such as physics, chemistry and biology.
Paramagnets are substances that are magnetized in an external magnetic field in the direction of the external magnetic field. In EPR spectroscopy, radio spectrometers are used, the schematic block diagram of which is shown in Fig. 1.
Rice. one. Block diagram of an EPR spectrometer. K - source of microwave radiation, V - waveguides, R - cavity resonator, D - microwave radiation detector, U - amplifier, NS - electromagnet, P - recording device.
The sample, which can be in any state of aggregation, is placed in a constant magnetic field and the study begins. In the process of recording the spectrum, the integrity of the substance is preserved, and it can be subjected to further research. In serial devices, the frequency of electromagnetic radiation is set constant, and the resonance condition is achieved by changing the magnetic field strength. Most of the spectrometers operate at a frequency of V=9000 MHz, a wavelength of 3.2 cm, and a magnetic induction of 0.3 T. Microwave electromagnetic radiation from a source (K) through waveguides (B) enters a cavity resonator (P) containing the sample under study and placed between the poles of an electromagnet NS.
Under resonance conditions, microwave radiation is absorbed by the spin system. The absorption-modulated microwave radiation is fed through the waveguide (B) to the detector (D). After detection, the signal is amplified at the amplifier (U) and fed to the recording device (P) in the form of the first derivative.
The EPR method makes it possible to obtain important information about the magnetic properties of a substance, and since the magnetic properties of a substance are directly dependent on its molecular structure, the EPR method is very promising for studying the structure of substances.
The magnetic properties of a substance are determined by the magnetic moments of elementary charged particles - electrons and protons, which are part of the atoms and molecules of the substance. Due to rotation around their own axis, these particles have a spin magnetic moment. Moving in an atom or molecule in a closed orbit, electrons acquire an orbital magnetic moment. Since the intrinsic magnetic moment of the proton is about 1000 times less than the spin magnetic moment of the electron, the magnetic moments of atoms, molecules, and macroscopic bodies are determined mainly by the spin and orbital moments of electrons [Dindoin, 1973].
Paramagnetic properties are possessed by ions of elements that have partially filled inner electron shells, for example, ions of transition elements of the D.I. Mendeleev (titanium, vanadium, copper, etc.). Transition elements are those in which electrons begin to fill the outer (valence) shell ( s-orbital) before the inner d- and f-shells are filled. The electronic configuration of metallic vanadium is: 3d 3 4s 2 . Its other valence states are also possible: +2 3d 3 4s o - paramagnetic;
electron paramagnetic resonance oil
V +3 3d 3 4s o - paramagnetic, due to the fact that both electrons have the same directed spins; +4 3d 3 4s o - paramagnetic; +5 3d 3 4s o - diamagnetic
In addition to the above groups, a small number of molecules with an even number of electrons, but not compensated, have paramagnetic properties (for example, an oxygen molecule, which is the simplest biradical - two of its valence electrons have parallel spins), as well as some atoms with an odd number of electrons, the so-called active atoms - H, O, N, Na, Ka, which under normal conditions cannot exist in the atomic state.
A small group of paramagnets is made up of color centers - F-centers containing uncompensated spins. F-centers are defects that impart a visible color to crystals that, in the absence of defects, would be colorless.
The color is due to two states of electrons or their energy levels, the energy difference of which is equal to the photon energy (frequency υ lies in the visible region of the spectrum).
In the absence of an external magnetic field, due to the chaotic thermal motion of particles, their magnetic moments are randomly directed, and there is either no interaction at all between the carriers of magnetic moments, or there is a very weak interaction, and the resulting moment is practically zero [Unger, Andreeva, 1995].
When an external constant magnetic field is applied, paramagnetic particles acquire a certain direction (parallel or antiparallel to the external field).
In this case, the Zeeman phenomenon occurs, which consists in the decoupling of the main energy level of the particle into (2s + 1) sublevels, separated from each other by energy intervals equal to:
∆E = gβH,
where s - quantum number particles (in the case of one uncompensated electron, s = ½); g is the factor of spectroscopic decoupling of a paramagnetic particle; β - the magnetic moment of the electron, due to the presence of spin and equal to 0.9273 * 10 -20 erg / e. H is the strength of the constant magnetic field in oersteds.
The distribution of electrons over sublevels occurs in accordance with the Boltzmann law:
where n 1 and n 2 - the number of electrons, respectively, at the upper and lower energy levels; K is the Boltzmann constant; T is the absolute temperature. According to this law, n 2 is always greater than n 1 by an amount that depends on the type of paramagnetic particle (in the case of one uncompensated electron, this difference is about 0.2%).
The essence of the discovery of the scientist Zavoisky E.K. consisted in the fact that when applying to a paramagnetic sample placed in a constant magnetic field, an alternating magnetic field with a frequency υ directed perpendicular to the constant magnetic field, provided that:
where h is Planck's constant (or quantum of action), equal to 6.624 * 10 -27 erg * sec; υ is the frequency of the electromagnetic field in hertz; electron transitions between two neighboring levels are induced with equal probability [Unger, Andreeva, 1995].
Since the levels are differently populated, the number of energy absorption events will exceed the number of stimulated emission events, and as a result, the substance will absorb the field energy. And with such absorption, the population of the levels n 1 and n 2 will tend to equalize, which leads to a violation of the Boltzmann distribution equilibrium. The process of absorption of ultrahigh frequency energy (hereinafter referred to as microwave) would immediately stop and the EPR spectrum would not be registered if there were no other mechanism that returns electrons from the upper level to the lower one. The mechanism of these uninduced transitions is associated with relaxation processes that also operate in the absence of a microwave field. The phenomenon of spin-lattice relaxation consists in the transfer of excess electron energy to thermal vibrations of the environment, called the "crystal lattice". The process of redistribution of excess energy between the electrons themselves is called spin-spin relaxation. The rates of these processes are characterized by the spin-lattice relaxation time T 1 and the spin-spin relaxation time T 2 . In systems with relatively long relaxation times, the leveling of the populations of energy levels occurs much faster than relaxation processes, and the phenomenon of signal saturation is observed already at relatively low power levels of microwave radiation. In the case of short relaxation times, the signal does not saturate at all, even at high powers of radio frequency energy [Unger, Andreeva, 1995].
Equipment
Devices that record EPR spectra are called radio spectrometers (Fig. 2). For technical reasons, in modern radio spectrometers, the frequency of the alternating magnetic field is maintained constant, and the strength of the static magnetic field is measured over a wide range [Belonogov, 1987]. A klystron is used as a microwave generator. The most widely used frequency is about 9000 MHz. This area is called the X-band (wavelength 3.0-3.5 cm). In addition to this region, higher frequencies are also used: K-band with a wavelength of 1.2-1.5 cm, and I-band with a wavelength of 0.75-1.20 cm. The microwave oscillations generated by the klystron are transmitted along the waveguide into a cavity resonator, in which the ampoule with the test sample is placed. This resonator is located between two poles of a large electromagnet in such a way that the static and alternating magnetic fields acting on the sample are mutually perpendicular. If, at a fixed frequency of an alternating magnetic field, we change the current in the winding of an electromagnet and thereby change the magnetic field strength, then when resonance conditions are reached, energy absorption can be observed. An approximate diagram of the device is shown in Fig.3.
To record spectra in modern radio spectrometers, the double modulation method is used, which makes the device noise-resistant to external shocks and vibrations and increases the sensitivity of the device. The double modulation method makes it possible to achieve that the resonant absorption curve is written in the form of the first derivative.
As additional equipment for calibrating the magnetic field sweep, a tracking intensity meter is used.
Of all currently existing methods for the detection and identification of free radicals, the EPR method is the most sensitive. The advantage of the EPR method over other static methods of magnetic measurements is that the measurement results are not affected by the diamagnetism of the molecules in the system. The sensitivity of modern domestic radio spectrometers, such as: RE-13-01, EPA-2, EPA-3, EPA-4, EPR-3, expressed in terms of the minimum detectable number of particles, is 10 11 - 10 12 paramagnetic particles.
Rice. 3. The device of the radio spectrometer:
microwave generator; 2 - waveguides; 3 - resonator; 4 - Electromagnet;
Detector; 6 - amplifier; 7 - recording device.
Samples studied by the EPR method can be in any state of aggregation. In the process of recording the spectrum, the integrity of the substance is preserved, and it can be subjected to further research. When recording the spectrum, the sample is usually placed in a glass ampoule that does not give an EPR signal. Since the glass of the ampoules reduces the quality factor of the device, the wall thickness of the ampoules should be as small as possible. If quartz glass is used, then the loss of microwave energy is negligible. The ampoule must be immersed in the resonator to such a depth that the entire sample is in the center of the microwave energy beam. In accordance with this requirement of the experiment on domestic radio spectrometers, the height of the sample layer in the ampoule should not exceed one centimeter. The outer diameter of the ampoule is usually 3-5 mm [Dindoin, 1973].
EPR spectrum parameters
The main task in observing the EPR signal is to accurately record the absorbed high-frequency energy. The spectrum is recorded in the coordinates: I abs = f (H) at υ = const, where I abs is the integral amplitude of the absorption of high-frequency energy; H is the strength of the constant magnetic field; υ - frequency of microwave energy. (Fig. 4).
From the analysis of the EPR spectrum, the following data can be obtained: the width and shape of the line, g-factor, the integral amplitude of the signal, the hyperfine structure of the spectrum, the width of the derivative of the absorption line, which is determined by the distance between the inflection points of the curve in oersteds. The physical meaning of this parameter is that, due to the Heisenberg uncertainty relation, it is inversely proportional to the lifetime of a paramagnetic particle in an excited state. This time is a criterion for the possibility of observing the EPR spectrum. At short times, the line is strongly broadened and cannot be observed experimentally. The line shape is mathematical expression dependence of the absorption intensity on the magnetic field strength. Line shapes described by the Lawrence or Gaus equations are rare in practice. For organic free radicals, they are usually intermediate, which is associated with the rapid movements of paramagnetic particles relative to each other, with the delocalization of unpaired electrons and their exchange effect. Since the width and shape of the line characterize the details of the structure and some features of the interaction of paramagnetic particles with each other and with environment, it is important to know the line shape of the test sample. For the correct determination of the concentration of paramagnetic particles, this is also of great importance. Of the existing methods, the simplest and at the same time accurate and effective way to analyze the shape of a line is to build linear anamorphoses according to experimental data, based on theoretical formulas. The spectroscopic splitting factor (g factor) is equal to the ratio of the magnetic moment of an uncompensated electron to the mechanical moment [Dindoin, 1973]. In essence, the g-factor is the effective magnetic moment of the particle, determining the measure of the influence of the orbital magnetic moment on the spin. For a free electron, when spin magnetism takes place, g is 2.0023. If an electron in a paramagnetic sample has a non-zero orbital momentum, then its orbital magnetic moment will add up to its own, giving the resulting momentum. Due to such spino-orbital action, the value of the g-factor will be different from 2.0023.
As a rule, the integral amplitude of the signal, other things being equal, is proportional to the number of paramagnetic centers in the sample. But, since often an experiment to determine the concentration of paramagnetic particles is carried out with samples and standards having different line widths and shapes, in the general case it is necessary to know the area under the resonance absorption curve. Modern radio spectrometers record the first derivative of this curve, so a double integration must be performed to determine the area. The use of integrals greatly simplifies this task, but so far not all radio spectrometers are equipped with them, and graphical double integration and somewhat facilitated integration using a nomogram are laborious and very inaccurate methods.
So, knowing the area under the resonance absorption curves for the test sample and the standard, recorded under the same conditions, we can calculate the number of paramagnetic centers in the test sample using the formula:
x \u003d N floor * [pmts],
where N x and N ref - the number of paramagnetic centers (PCC) in the test sample and standard, respectively; A x and A floor - the area under the absorption curves for the test sample and standard, respectively.
In the case when the experiment is associated with taking the spectra of a series of samples of the same type, having the same shape lines with a standard with a changing signal width, in the formula, instead of areas, the product of the integral amplitudes by the squares of the line width is taken:
where I is the signal amplitude; H - signal width, N - OPC in the reference. In this case, the indices "at" refer to the main standard, "x" - to the test sample, "Ci" - to the auxiliary standard (CuSO 4 * 5H 2 O).
In this case, the CPV is calculated in 1g of the substance, by dividing the result by the weight of the test sample.
If the shape of the line of the standard is different from the shape of the line of the series of identical samples under study, it is necessary to enter a correction factor. Otherwise, the maximum error (when one line is Lorentzian and the other Gaussian) reaches ±38%, but it will always be systematic. Due to the imperfection of the equipment and methods for preparing standards, the accuracy of absolute measurements is 30-40%. In the case of measurements in relative units, the accuracy of the method will increase with two - and three-fold removals up to 3-10%.
Hyperfine structure (HFS) of EPR spectra
If the paramagnetic system under study contains atoms with nuclear magnetic moments (H 1, D 2, N 14, C 13 and others), then due to the interaction of electronic and nuclear magnetic moments, a hyperfine structure of the EPR line arises - the line, as it were, splits into several components.
For aromatic free radicals, there is an important empirical dependence of the proton hyperfine uncoupling constant on the unpaired electron density on the neighboring carbon atom. Thanks to this, it is possible to determine from the experiment the density of an unpaired electron on the corresponding atoms, which allows one to directly judge the reactivity of various sites in the radicals.
The study of SFS in paramagnetic ions makes it possible to determine, by the number of components, the spin of the nucleus and judge its magnetic moment.
One of the most important elements, the EPR spectrum, which is hyperfine, is V +4 . In a large group of oils, a complex structure of the resonance absorption line is found, due to the presence of a paramagnetic ion V +4 in them. In oils, V +4 is associated with porphyrins, resins, and is included in the structure of asphaltenes. The vanadium ion easily forms tetrapyrrole compounds as a result of catagenesis (Fig. 5.). The V+4 TS spectrum consists of eight lines. The central of these eight lines (component 5) with the projection of the nuclear spin is anomalously large in comparison with other HFS components (Fig. 6.)
As a result, developed effective method determining V +4 in oils and its fractions by the integral amplitude of this anomalous component of the spectrum, the calculation formula is as follows:
where is the number of paramagnetic centers in the standard; - integral amplitude of the fifth component of the STS V +4 in mm; - width of the fifth component in mm; - integral amplitude and width of the standard in mm; a- weight of the test sample in g [Dindoin, 1973].
Rice. 6. Hyperfine structure of the V+4 spectrum.
Factors affecting the feasibility of using the EPR method
Experimental data were considered in [Bartashevich, 1975] to determine the factors affecting the EPR carbon signal of sedimentary rocks. The measured samples from the collection gave OPV values per 1g of rock from 0.2*10 17 to 15*10 17 . If these values are arranged depending on the percentage of Corg in the rock, then for most samples there is a direct relationship, which implies that the first factor affecting the intensity of the EPR carbon signal is the content of Corg in the rock. In some cases, deviations from this basic pattern are revealed, the analysis of which shows the presence of two more factors affecting the intensity of the EPR signal. In cases where the rock taken was oil-saturated samples, the signal amplitude was insignificant, while the Corg content reached 1% or more. In these cases, according to the chemical-bituminological analysis, the organic matter consists of more than 50% of bituminous components.
The second factor is the influence that the group composition of organic matter dispersed in the rock, that is, the quantitative ratios of bituminous and non-bituminous components, has on the EPR signal value. In the case when bituminous components predominate in the OM balance, the signal is insignificant, since the bituminous components isolated from the rock have an order of magnitude fewer paramagnetic centers than the number of insoluble OM components. If non-bituminous OM components form the basis of organic matter, the signal increases.
The third factor that influences the EPR signal is the change in the degree of OM metamorphism. So, for example, in Paleogene clays taken from a depth of 150-200 m with a Corg content of 1.8 CPC, it was 0.2*10 17 CPC/g. In similar sediments taken from a depth of 1500-1700 m, with a lower Corg content (0.4%), the PCC remained almost the same - 0.3*10 17 . It is obvious that with an increase in the degree of metamorphism, the OM structure is rearranged, which entails an increase in the CFC.
The obtained regularities about the influence of three main factors on the EPR signal of organic matter in the rock to some extent limit the use of the EPR method for complex geological reserves in which the amount, composition and degree of metamorphism of OM change. Since the content of Corg is only one of the three factors affecting the magnitude of the carbon signal, the establishment of regularities in the location of OM by the EPR method is possible only under conditions that ensure the invariance of the other two factors. Such conditions take place in a single lithostratigraphic complex.
In the problem of studying oil and gas formation and prospecting for oil and gas deposits, it is fundamentally importance have geochemical studies of organic matter in rocks. The first stage of these studies is the mass determination of OM from well sections.
The high sensitivity and rapidity of the analysis of the studied samples without destruction determine the prospects of the EPR method for establishing geochemical patterns in well sections.
Application of the EPR method
When observing an EPR signal, the main task is to accurately record the absorbed high-frequency energy. The spectrum is recorded in coordinates I absorb= F (H) with V=const, where I absorb - integral amplitude of absorption of high-frequency energy; H is the strength of the constant magnetic field, V is the frequency of the microwave energy. By the peaks on the spectrum, it is possible to determine the number of aromatic structures, the type and amount of free radicals. The concentration of paramagnetic centers (PCCs) in resins, asphaltenes, and kerogens is approximately one order of magnitude, 10 19 kpc/g. substances. The intensity of the absorbed energy is proportional to the CPC and is related to the Corg index: the higher the intensity, the higher the Corg, respectively. There are works that have shown the relationship between EPR data and the geological conditions of oil formation. It is shown that in oils of deep-lying deposits (1000-2000-2800 m.) CPC increases with depth, and for oils occurring at shallow depths, the dependence is inverse (Fig. 7).
Rice. 7. Change in CPC with increasing depth of immersion, grams * 10 19
The study of the residual OM of sedimentary rocks by the EPR method was first undertaken by a team of researchers led by K.F. Rodionova in order to elucidate the possibilities of the method for assessing the nature of OM, the initial source for the formation of oil. The results of subsequent studies, including those of other authors, show that the OPC varies depending on the type and metamorphism of sedimentary OM. By chemical methods two main types (humus and sapropel) and intermediate types of residual OM were established. It turned out that each type is characterized by a quite definite and unique character of the dependence of the concentrations of paramagnetic centers on the carbon content. Therefore, to determine the type of OM of sedimentary rocks and the degree of its transformation, along with chemical methods, the EPR method is used, and it is not only a completely acceptable quantitative criterion for the degree of kerogen diagenesis, but also more accurate than the results of IR spectroscopy.
According to all the previous results of studies of NOR, the concentration of paramagnetic centers (PCC) in kerogen varies depending on its type and the degree of catagenetic transformation. For example, it has been established that the narrower , the more kerogen is converted. Kerogens have about 10 19 paramagnetic centers per gram of substance (Dindoin, 1973).
Thus, the change in EPR parameters is used in geochemistry in the study of kerogens of various genetic types and the degree of catagenetic transformation. It is important that this method is not destructive, that is, the integrity of the substance is preserved in the process of recording the spectrum, and it can be subjected to further research.
Determination of the Genesis of Dispersed Organic Matter and Oils
The study of the residual OM of sedimentary rocks by the EPR method was first undertaken by a team led by Rodionova K.F. [Bartashevich, 1975] in order to clarify the possibilities of the method for assessing the nature of OM, the initial for the formation of oil. The results published in this work showed that the OPC varies depending on many factors, the main one being the type of metamorphism of sedimentary OM. Two main (humus and sapropel) and intermediate types of residual OM were identified chemically. It turned out that each type is characterized by a quite definite and unique character of the dependence of the OPC on the carbon content.
Interesting results on the use of the EPR method in determining the type of OF were obtained by L.S. Borisova (Borisova, 2004) in the study of DOM asphaltenes of various genetic nature. Continental lacustrine-swampy and lacustrine-alluvial sediments of the Lower-Middle Jurassic (Tyumen Formation) and Lower (Aptian-Albian) - Upper (Cenomanian) Cretaceous (Pokursk Formation) of the West Siberian megasyneclise, aquatic ( sapropel) OM - Bazhenov suite (J 3 v) and its age analogs. There are, on average, less free radicals in the structure of asphaltenes of aquatic OM (5*10 17 PMC/g) than in TOA asphaltenes (12*10 17 PMC/g), which is consistent with a higher degree of aromaticity and low values of H/C at of bitumoid asphaltenes coal-bearing strata. (fig.8)
For me, the work of the staff of the IPGG SB RAS L.S. Borisova, L.G. Gilinskaya, E.A. Kostyreva et al. "Distribution of V +4 in asphaltenes of oil-producing rocks and oils of Western Siberia" [Borisova et al., 1999].
The results of this work showed that in asphaltenes DOM of the Abalanskaya Formation V +4 is present in very small amounts (the maximum content is 0.1 rel. units). In addition to vanadium, trivalent iron was also found. Asphaltene samples from the Bazhenov Formation show a high concentration of V +4 (the maximum value is 35 rel. units), and it depends on the host rocks: in Bazhenovites, the content of V +4 is 5–10 times higher than in mudstones.
Thus, a comparative study in (Borisova et al., 1999) of asphaltenes from the DOM of the Bazhenov and Abalak Formations showed that V +4 accumulated in significant amounts in the deposits of the Bazhenov Formation, which formed in the sea basin under conditions of hydrogen sulfide contamination. The content of V +4 in the Abalak Formation is extremely low (Fig. 9).
Rice. Fig. 9. Distribution of V +4 in asphaltenes and asphaltene acids DOM B - Bazhenov formation; A - Abalak Formation (Borisova et al., 1999).
Also, the presence of V +4, determined by the EPR method, can serve as an indicator or "genetic label" of oils. It has been experimentally proven that highest value V +4 is noted in the Cretaceous and Upper Jurassic oils of the central part of Western Siberia (Fig. 10). These are C1 type oils (according to the classification of A.E. Kontorovich and O.F. Stasova [Borisova, 2009]) genetically associated with marine deep-water sediments. Oils of type A 1 practically do not contain V + 4 , and its presence is observed only in individual samples in small quantities. In the Lower-Middle Jurassic sequence, according to the content of vanadium, L.S. Borisova identified two types of oils: low-sulphur oils of the Krasnoleninsky arch and northern regions of Western Siberia (type A 2 and A 1 , respectively), which have low values of V + 4 and high-sulphur oils of the Yugansk depression (type C 2), the content of asphaltenes in which is significant [ Borisova et al., 1999] In addition, there is a clear relationship between the content of V +4 in asphaltenes and sulfur in oils. Thus, the highest sour oils of the marine type have the highest values of V +4 content. Low-sulfur oils contain practically no or negligible amounts of V +4.
This suggests that favorable conditions for the accumulation of vanadium, porphyrins, and sulfur occur at the bottom of steadily sinking basins with uncompensated sedimentation and a stagnant marine regime (Borisova, 2009).
Conclusion
As can be seen from the foregoing, the EPR method is of great importance for organic geochemistry. This method has very important qualities that provide its advantage over other methods, namely:
Rapid analysis
Carrying out analysis without the slightest chemical intervention
Analysis Accuracy
Ease of detection of vanadium ions, which helps us to judge the genesis of this organic matter.
Using the EPR method, asphaltenes of modern sediments are studied in order to reveal the evolution of tetrapyrrole pigments, DOM asphaltenes are studied when diagnosing oil source strata (in particular, when determining the type of OM), the effect of the degree of catagenesis in DOM asphaltenes on OPC is studied, the paramagnetic properties of oils (Vanadium CTC) are studied, study the paramagnetism of coals, investigate the EPR parameters of keragen depending on catagenesis, and much more.
In the process of writing term paper, I learned how to work with scientific literature, structure the knowledge gained and present it in the form of abstract work.
Bibliography
1. Bartashevich O.V. Geological methods exploration of oil and gas fields. Moscow. VNIYAGG, 1975, 30s.
2. Belonov A.M. Magnetic resonance in the study of natural formations. Leningrad "Nedra" Leningrad branch 1987, 191 p.
Borisova L.S. Geochemistry of asphaltenes in Western Siberia oils / L.S. Borisov // Geology of oil and gas - 2009 - No. 1. - p.76-80.
Borisova L.S. Heterocyclic components of dispersed organic matter and oils of Western Siberia // Geology and Geophysics. - 2004. - No. 7. - pp. 884-894.
Borisova L, S., Gilinskaya L.G., E.A. Kostyreva et al. Distribution of V +4 in asphaltenes of oil-producing rocks and oils of Western Siberia / Organic geochemistry of oil-producing rocks of Western Siberia: proc. report scientific Meetings / IGNG SB RAS. - Novosibirsk, 2009. - pp. 147-149.
Dindoin V.M. Modern methods analysis in organic geochemistry. Proceedings of SNIIGGIMS 2008, issue 166, 23 p.
Unger F.G., Andreeva L.N. Fundamental aspects of petroleum chemistry. Novosibirsk, VO "Nauka", 2012, 187 p.
The phenomenon of magnetic resonance. Electron paramagnetic resonance (EPR)
In the previous section, we considered the splitting of spectral lines associated with transitions between sublevels of different energy levels split in a magnetic field. Such transitions correspond to the optical frequency range. Along with this, in the dipole approximation, transitions between neighboring sublevels of an energy level split in a magnetic field are possible according to the selection rules:
From formula (3.95) it follows that such transitions correspond to frequencies:
At AT~ 0.3 T frequency v * 10 Hz, and the wavelength X~ 3 cm. This is the microwave frequency range, or the microwave range. The probability of dipole transitions is proportional to v 3 ; therefore, in the microwave range it is negligibly small compared to the probability in the optical range. In addition, for atoms with one valence electron, transitions in this case are forbidden by the selection rule AL=±. However, the transition probability becomes significant when an additional external alternating magnetic field is applied, i.e., when the transitions become forced. It will be clear from what follows that the alternating magnetic field must be perpendicular to the stationary magnetic field, which causes the Zeeman splitting of the energy levels. If the frequency of the alternating magnetic field is equal to the transition frequency (3.101), then its energy is absorbed or stimulated emission occurs. In this case, the orientation of the magnetic moment of the atom, i.e., its projection onto the selected direction, changes abruptly.
The emission or absorption of electromagnetic waves when the orientation of the magnetic dipole moments of atoms in a magnetic field changes is called the phenomenon of magnetic resonance.
A consistent description of magnetic resonance is quite difficult. A qualitative picture of this phenomenon can be understood on the basis of a simple classical model. If a particle has a magnetic moment M, then in an external constant magnetic field B 0 = (0.0, B 0) a torque acts on it K \u003d MxV 0. Since the magnetic M and mechanical J moments of a particle (for example, an electron in an atom) are related by the relation:
where y is the gyromagnetic ratio, y = gib /h = eg/2m e , then the equation of motion can be written as:
This is the top equation, which shows that the mechanical and magnetic moments precess around B 0 . The angular velocity (frequency) of this precession is:
In a magnetic field directed along the axis z, the particle acquires additional energy:
The transition frequency between adjacent energy sublevels coincides with the precession frequency:
Rice. 3.34
If we add a magnetic field B changing with frequency w, perpendicular to the stationary field B 0 (Fig. 3.34), then an additional variable torque [MxV, 1. When the frequencies of precession and field change B! differ strongly from each other, then as |B, |z, so that on average this angle does not change. However, if the frequency of the change in the field B coincides with the precession frequency (3.104), then the magnetic moment appears to be in static conditions, as it were, and the additional torque tends to “overturn” it. Since the magnetic moment is a quantum vector, its projection onto the direction of the static magnetic field can only change abruptly, which corresponds to the transition to the neighboring split sublevel. This is the phenomenon of magnetic resonance.
If the magnetic and mechanical moments of an atom are due to its electrons, then in this case magnetic resonance is called electron paramagnetic resonance(EPR). When the moments are determined by the nucleus of an atom, then magnetic resonance is called nuclear magnetic resonance(NMR), which was first observed in experiments with Rabi molecular beams in 1938. There are also ferromagnetic and antiferromagnetic resonances associated with a change in the orientation of the electronic magnetic moments in ferromagnets and antiferromagnets. Next, let's take a closer look at EPR.
Electronic paramagnetism is possessed by: all atoms and molecules with an odd number of electrons (unpaired, uncompensated electrons) on the outer electron shells, since in this case the total spin of the system is not equal to zero (free sodium atoms, gaseous nitric oxide, etc.); atoms and ions with an unfilled inner electron shell ( rare earth elements, actinides, etc.), etc. EPR is a set of phenomena associated with quantum transitions occurring between the energy levels of macroscopic systems under the influence of an alternating magnetic field of resonant frequency.
The EPR phenomenon was first observed experimentally by E. K. Zavoisky in 1944. EPR is a powerful tool for studying the properties of paramagnetic substances in macroscopic quantities. In this case, there is not one, but many particles with magnetic moments. The macroscopic magnetic characteristic of a substance is the magnetization vector 1 = , where N- number of particles per unit
the volume of the substance; is the average magnetic moment of the particles. The system of moments of all paramagnetic particles of a given substance is called the spin system. The remaining degrees of freedom of a paramagnet - the environment of magnetic moments - are called the "lattice". In this regard, two types of interaction are considered: magnetic moments with each other (spin-spin interaction) and magnetic moments with their environment (spin-lattice interaction). In an isolated spin system, there is no stationary absorption of the energy of the alternating field. Indeed, before switching on the alternating magnetic field, the number of particles in the ground state is greater than their number N 2 in an excited state. When energy is absorbed, the number of particles JV decreases, and the number N 2 increases. This will happen until N] and N 2 are not equal. Then saturation is reached, and further absorption of energy stops. Taking into account the interaction of the spin system with the lattice, stationary energy absorption becomes possible. The grate serves as an energy sink and heats up in the process.
The change in the magnetization vector is described by the Bloch equation:
where a = (x,y,z)‘ t y - gyromagnetic ratio; 1 0 - equilibrium value of the magnetization vector in a constant magnetic field in 0 =(0,0, at 0); t x - spin-spin (or transverse) relaxation time, t x \u003d t y=t 2 ; t z - spin-lattice (or longitudinal)
relaxation, m^ = m,. The values of m and m 2 depend on the characteristics of the interaction of each particle with the particles surrounding it. Determination of these relaxation times is the main experimental problem of the magnetic resonance method. In the equation
(3.106) the first term is written by analogy with the equation of motion of a single magnetic moment (3.103). The second term is due to spin-spin and spin-lattice interactions, which determine the achievement of an equilibrium state by the system.
The radiation power /(co) absorbed by the paramagnetic substance is calculated using equation (3.106). It is defined by the formula
where BUT- some multiplier; AT ]- amplitude of the alternating magnetic field. The shape of the absorption curve is determined by the function
where o) 0 - frequency of precession, o) 0 =y# 0 .
This shows that the absorption is resonant in nature (Fig. 3.35). The absorption curve has a Lorentzian shape and reaches a maximum at resonance: co=co 0 . Absorption line width:
In a sufficiently weak high-frequency magnetic field, the width of the absorption curve is determined by the spin-spin relaxation time. As this field increases, the absorption line broadens. The width of the absorption curve determines the relaxation times, which are associated with the properties of the substance. To achieve resonance in experiment, it turns out to be more convenient to change not the frequency o of the alternating magnetic field, but the frequency of the precession by changing the constant magnetic field.
On fig. 3.36 shows one of the simple schemes of a radio spectroscope for observing EPR - a radio spectroscope with a waveguide bridge. It contains a stable source of RF radiation - a klystron, a tuned cavity resonator with the sample under study, and a measuring system for signal detection, amplification, and indication. The energy of the klystron goes half to the arm of the resonator containing the test sample, and half to the other arm to a matched load. When adjusting with a screw, the bridge can be balanced. If then, with the help of modulation coils, the constant magnetic field is changed, then at resonance, the absorption of energy by the sample increases sharply, which leads to an unbalance of the bridge. Then, after amplifying the signal, the oscilloscope writes a resonant curve.
The EPR method has a high sensitivity. It allows you to measure relaxation times, nuclear magnetic moments, carry out a quantitative analysis of any paramagnetic substances up to 10 -12 g of a substance, and determine the structure of chemical compounds.
electronic configurations, measure weak magnetic field strengths up to 79.6 A/m, etc.
Let us show how it is possible to calculate the power of radiation absorbed by a paramagnetic substance (3.107). Let us represent an alternating magnetic field rotating clockwise (in the direction of the precession of the magnetic moment) in complex form:
B(t)== 2?,coso)/-/"#, sinw/ = 2? u +iBly . You can also enter
complex magnetization vector /(/)= / and + and ( 9 which is related to the complex vector of the alternating magnetic field by the relation / = x(o>)H, where x(w) is the complex magnetic susceptibility. This relation is introduced similarly to the static case, when the magnetic field BQ constantly: / 0 = x 0 ? 0 , where %o~ static magnetic susceptibility. From the Bloch equations (3.106) we obtain
In the steady state we have: - = - / o) /, - = 0. Then from
system (3.110) follows the system of equations:
Solution for this system:
The average absorbed power over the period of the field can be calculated by the formula
Hence it follows that the absorbed power is determined by the imaginary part of the complex magnetic susceptibility.
Many fundamental results have been obtained using the magnetic resonance method. In particular, the anomalous magnetic moment of the electron was measured. It turned out that the spin magnetic moment of an electron is not equal to exactly one Bohr magneton, i.e., for an electron, the gyromagnetic ratio g e ^2. This has already been discussed in §2.7. The magnetic moment of the neutron was also measured, etc. Based on this method, an atomic beam standard for frequency and time was created - atomichron using a beam of cesium atoms Cs 133
1. In the free Cu 2+ ion, one electron is missing in the 3^ shell. Determine the frequency of paramagnetic resonance in a magnetic field 421.88-10 3 A/m.
Solution. Main state - /)-state (L= 2) with spin 5= 1/2. According to Hund's rule, the number /= L+ 5=5/2. In the absence of a magnetic field, this level is not split with the degeneracy factor (25+ 1)(2Z.+ 1)= 10. In a constant magnetic field, the level splits into 2/+ 1 = 6 sublevels. Lande factor g=6/5. The paramagnetic resonance frequency is determined by formula (3.101).
EPR
Principle of the EPR method
The history of the discovery of the EPR method
EPR method is the main method for studying paramagnetic particles present in biological systems. Paramagnetic particles of great biological importance include two main types of compounds - these arefree radicals and variable valence metals (such as Fe, Cu, Co, Ni, Mn) or their complexes. In addition to free radical states, the EPR method is used to study triplet states that arise in the course of photobiological processes.
The method of electron paramagnetic resonance was discovered relatively recently - in 1944 . at Kazan University by Evgeny Konstantinovich ZAVOYSKY in the study of the absorption of electromagnetic energy by paramagnetic metal salts. He noticed that a single crystal CuCl 2, placed in a constant magnetic field of 40 Gauss (4 mT) begins to absorb microwave 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 published an article in 1958 in the journal Biophysics on the study of free radicals produced by the action of ionizing radiation on proteins.
Mechanical and magnetic moments of an electron
The orbital and spin motion of electrons underlie their orbital and spin mechanical moments. Orbital angular momentum of an electron R along an orbit of radius R equals:
Where I is the current in the circuit, and S - the area of the contour (in this case, the circular orbit is equal to pR2 ). Substituting in formula (2) the expression for the area and taking into account that:
Comparing the expressions for the mechanical and magnetic moments of the electron (1) and (4), we can write that:
Where n - orbital quantum number, which takes the values 0, 1, 2 and m In this case, taking into account (6), the expression for the magnetic orbital moment will look like:
The spin magnetic moment of an electron is associated with the spin motion of an electron, which can be represented as a motion around its own axis. The spin mechanical moment of an electron is equal to:
|
|
Where S - spin quantum number equal to 1/2 .
The magnetic and mechanical spin moments are related by the relation:
|
| (10) |
Where MS
- magnetic quantum number, equal to +1/2
. The ratio of the magnetic moment to the mechanical moment is called the gyromagnetic ratio ( g
). It can be seen that for orbital motion: 
, and for the spin: 
For the gyromagnetic ratio of electrons with different contributions of orbital and spin motion, the proportionality coefficient is introduced g
, such that:
|
| (11) |
This proportionality factor is called g -factor. g =1, at S =0, i.e. when there is no spin motion of the electron and only orbital motion exists, and g =2 if there is no orbital motion and only spin motion exists (for example, for a free electron).
The magnetic moment of an electron is generally composed ofspin and orbitalmagnetic moments. However, in most cases, the orbital magnetic moment is zero. Therefore, when discussing the principle of the ýïr method, onlyspin magnetic moment.
Zeeman effect
The energy of interaction of the magnetic moment of an electron with a magnetic field is expressed by the equation:
| (12) |
Where m H - magnetic field strength, cos( mH ) is the cosine of the angle between m and H .
Zeeman effect (Fig. 1) ( ES =+1/2 and ES =-1/2 )
From equation (11) it follows that:
In this case, the difference in energy between the two levels will be:
|
| (15) |
Equation (14) 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.
Basic resonance equation
The number of electrons having a particular energy will be determined in accordance with the Boltzmann distribution, namely:
If now an electromagnetic energy is applied to a system of electrons in a magnetic field, then at certain values of the energy of the incident quantum, transitions of electrons between levels will occur. A necessary condition for transitions is the equality of the energy of the incident quantum ( hn ) energy difference between the levels of electrons with different spins ( gbH ).
|
| (17) |
Equation (17) expresses the main condition for the absorption of energy by electrons. Under the influence of radiation, electrons that are at a higher energy level will emit energy and return to a lower level, this phenomenon is calledinduced emission.
The 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 in a given energy level, thenabsorption of energy will prevail over its emission . This is due to the fact that, as follows from equation (16), the population of the lower level is higher than the population of the upper energy level.
At this point, the special position of free radicals should be noted, i.e. molecules with unpaired electrons in the outer electron orbital in the distribution of electrons over energy levels. If there is a pair of electrons in the orbital, then naturally, the population of the energy levels will be the same and the amount of energy absorbed by the electrons will be equal to the amount of energy emitted.
The absorption of energy by a substance placed in a magnetic field will be noticeable only if there is only one electron in the orbit, then it will be possible to speak ofBoltzmann distributionelectrons between energy levels.
Characteristics of the EPR spectra
Signal amplitude
To determine the concentration, the areas under the absorption curve are measured for a standard with a known concentration of paramagnetic centers in the measured sample and an unknown concentration; is found from the proportion, provided that both samples have the same shape and volume:
|
| (18) |
Where C rev. and C this. - concentration measured sample and standard, respectively, and S rev. and S this. - area under the absorption lines of the measured signal and the standard.
To determine the area under the absorption line of an unknown signal, you can use the numerical integration method:
Where f(H) - first derivativeabsorption lines (EPR spectrum), F(H) - function absorption lines, and H - tension magnetic field.
Where f"(H) is the first derivative of the absorption line, or EPR spectrum . It is easy to pass from the integral to the intercal sum, given that H=n*DH , we get:
|
| (21) |
Where D.H. is the step of changing the magnetic field, and n i - step number.
Thus, the area under the absorption curve will be equal to the product of the square of the magnetic field step and the sum of the products of the EPR spectrum amplitude and the step number. From expression (21) it is easy to see that for large n (i.e. far from the center of the signal) the contribution of remote parts of the spectrum can be quite large even at small values of the signal amplitude.
Line shape
Although, according to the basic 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 not a line, but continuous in some neighborhood of the resonance point. The function describing the EPR signal is calledline shape function . In dilute solutions, when the interaction between paramagnetic particles can be neglected, the absorption curve is described by the Lorentz function:
The Gaussian function is envelope EPR spectrum if there is an interaction between paramagnetic particles. It is especially important to consider the line shape when determining the area under the absorption curve. As can be seen from formulas (22) and (23), the Lorentz function has a slower decrease 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) and electrons.
Let us consider the mechanism of energy absorption by unpaired electrons in more detail. If in the low energy state there is N 1 electrons, and in high-energy N 2 and N 1 more N 2, then when electromagnetic energy is applied to the sample, the difference in the level populations will decrease until it becomes equal to zero.
This is because the probabilities of a single transition under the action of radiation from a low-energy state to a high-energy state and vice versa ( W 12 and W 21) are equal to each other, and the population of the lower level is higher. Let's introduce a variable n =N 1 -N 2. Then the change in the difference in the level populations over time can be written:
and 
; where
| (24) |
However, in the experiment, no change in the level population difference is observed due to the fact that there are relaxation processes that maintain this difference constant. The relaxation mechanism consists in transferring a quantum of electromagnetic energy to the lattice or surrounding electrons and returning the electron to a low-energy level
If we denote the probabilities of lattice-induced transitions as P 12 and P 21 , and P 12 less P 21 , then the change in the level population difference will be:
In the stationary state, when the change in the population difference is zero, the initial difference in the level populations ( n 0) remains constant and equal to:
Or replacing P 12 +P 21 on 1/T 1 , we get
|
| (29) |
Value T 1 calledspin-lattice relaxation timeand characterizes the average lifetime of the spin state. As a result, the change in the population difference between the levels of the system of unpaired electrons, which is under the influence of electromagnetic radiation and interacts with the lattice, will be determined by the equation:
And at 2WT 1 much less 1 , n = n 0 , i.e. at relatively low powers, the level population difference remains practically constant . From the Heisenberg uncertainty relation it follows that:
|
| (32) |
If we accept that Dt equals T 1 , and DE corresponds gbDH , then equation (32) can be rewritten as:
|
| (33) |
Those. the linewidth uncertainty is inversely proportional to the spin-lattice relaxation time.
In addition to the interaction of the magnetic moment of an unpaired electron with the lattice, its interaction with the magnetic moments of other electrons is also possible. This interaction leads to a decrease in the relaxation time and thus to broadening of the line in the EPR spectrum. In this case, the concept of spin-spin relaxation time is introduced ( T 2). The observed relaxation time is considered to be the sum of the spin-lattice and spin-spin relaxation times.
For free radicals in solutions T 1 much less T 2 , so the line width will be determined by T 2. Among the mechanisms of line broadening, the following should be mentioned:dipole-dipole interaction; g-factor anisotropy; dynamic line broadening and spin exchange .
The dipole-dipole interaction is based on the interaction of the magnetic moment of an unpaired electron with the local magnetic field created by neighboring electrons and nuclei. The strength of the magnetic field at any point depends on the distance to this point and the mutual orientation of the magnetic moments of an unpaired electron and another interacting electron or nucleus. The change in the energy of an unpaired electron will be determined by:
| (34) |
Where m is the magnetic moment of the electron, R - distance to the source of the local magnetic field, q is the angle between interacting magnetic moments.
Anisotropy contribution g -factor in the broadening of the EPR line is due to the fact that the orbital motion of an electron creates an alternating magnetic field with which the spin magnetic moment interacts. This interaction leads to deviation g -factor of value 2,0023 correspondingfree electron.
For crystalline samples, the values g -factor corresponding to the orientation of the crystal denote g xx, g yy and g zz respectively. When molecules move quickly, for example in solutions, anisotropy g -factor can be averaged.
The broadening of the EPR signal may be due to the mutual transformation of the two forms of the radical. So, if each of the forms of the radical has its own EPR spectrum, then an increase in the rate of mutual transformation of these forms into each other will lead to line broadening, since in this case, the lifetime of the radical in each state decreases. This change in signal width is calleddynamic broadening of the signal. Spin exchange is another way to broaden the EPR signal. The mechanism of signal broadening during spin exchange consists in changing the direction of the spin magnetic moment of an electron to the opposite when it collides with another unpaired electron or another paramagnet.
Since such a collision reduces the lifetime of an electron in a given state, the EPR signal is broadened. The most frequent case of EPR line broadening by the spin exchange mechanism is signal broadening in the presence of oxygen or paramagnetic metal ions.
Hyperfine structure
The splitting of the EPR line into several is based on the phenomenon of hyperfine interaction, i.e., the interaction of the magnetic moments of unpaired electrons ( M S) with magnetic moments of nuclei ( M N).
|
| Since in the presence of the magnetic moment of the nucleus, the total magnetic moment is equal to M S+ M N , where M S is the magnetic moment of the electron, and M N is the magnetic moment of the nucleus, then the total magnetic field H amounts. = H 0 ± H lok. , where H lok. - local magnetic field created by the magnetic moment of the nucleus. |
An important feature of the hyperfine interaction is the selection rules for transitions between levels. Allowed transitions are transitions in which the change in the spin magnetic moment of an unpaired electron ( DM S) equals 1 , and the spin magnetic moment of the nucleus ( DM N) equals 0 .
In the example we have considered, the spin of the nucleus interacting with the unpaired electron was half-integer and was equal to ± 1/2, which eventually gave us a split into two lines. This spin is typical for protons . At the nuclei of nitrogen atoms ( N 14) integer spin. It can take values ±1 and 0 . In this case, when the unpaired electron interacts with the nucleus of the nitrogen atom, splitting into three identical lines will be observed, corresponding to the spin value +1 , -1 and 0 . In the general case, the number of lines in the EPR spectrum is equal to 2M N+ 1 .
Naturally, the number of unpaired electrons and, accordingly, the area under the EPR absorption curve do not depend on the magnitude of the nuclear spin and are constant values. Therefore, when splitting a single EPR signal into two or three, the intensity of each component will be, respectively, in 2 or 3 times lower.
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 other than zero, for example, two protons. In this case, three states arise corresponding to the orientation of the proton spins:
1. both on the field,
2. both against the field
3. one on the field and one against the field.
Option 3 is twice as likely as 1 or 2 , because can be done in two ways. As a result of such a distribution of unpaired electrons, a single line splits into three lines with the intensity ratio 1:2:1 . In general, for n equivalent nuclei with spin M N number of lines is 2nM N+ 1 .
EPR radio spectrometer device
The device of the EPR radio spectrometer in many ways resembles the device of a spectrophotometer for measuring optical absorption in the visible and ultraviolet parts of the spectrum.
The source of radiation in the radio spectrometer is the klystron, which is a radio lamp that gives monochromatic radiation in the centimeter wave range. The aperture of the spectrophotometer in the radiospectrometer corresponds to an attenuator that allows you to dose the power incident on the sample. The cuvette with the sample in the radio spectrometer is located in a special unit called the 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. The missing element in the optical spectrometer is an electromagnet that creates a constant magnetic field necessary for splitting the energy levels of electrons.
The radiation that has passed through the measured sample, in the radio spectrometer and in the spectrophotometer, hits the detector, then the detector signal is amplified and recorded on a recorder or computer. One more difference of the radiospectrometer should be noted. It lies in the fact that the radiation of the radio range is transmitted from the source to the sample and then to the detector using special rectangular tubes called waveguides. The cross-sectional dimensions of the waveguides are determined by the wavelength of the transmitted radiation. This feature of the transmission of radio emission through waveguides determines the fact that a constant radiation frequency is used to record the EPR spectrum in the radio spectrometer, and the resonance condition is achieved by changing the magnitude of the magnetic field.
Another important feature of the radio spectrometer is signal amplification by means of its modulation by a high-frequency alternating field. As a result of signal modulation, it is differentiated and the absorption line is converted into its first derivative, which is the EPR signal.
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 a difficulty, which consists in the low concentration of free radicals formed during the vital activity of cells. The concentration of radicals in normally metabolizing cells is, according to various sources, approximately 10 -8 - 10 -10 M , while modern radiospectrometers make it possible to measure the concentrations of radicals 10 -6 - 10 -7 M .
You can increase the concentration of free radicals by slowing down their death and increasing the rate of their formation. This can be done by irradiating (UV or ionizing radiation) biological objects at low temperatures.
The study of the structure of radicals of more or less complex biologically important molecules was one of the first areas of application of the EPR method in biological research.
EPR spectra of UV-irradiated cysteine
EPR spectrum of rat liver
Another important area of application of the EPR method in biological research was the study of metals of variable valence and/or their complexes that existin vivo.
If you look at the EPR spectrum, for example, of a rat liver, you can see the signals of cytochrome R-450 having g -factor 1,94 and 2,25 , methemoglobin signal with g -factor 4,3 and a free radical signal belonging to the semiquinone radicals of ascorbic acid and flavins with g -factor 2,00 .
Due to the short relaxation times, the EPR signals of metalloproteins can only be observed at low temperatures, such as liquid nitrogen.
However, the EPR signals of some radicals can also be observed at room temperature. These signals include the EPR signals of many semiquinone or phenoxyl radicals, such as the semiquinone radical of ubiquinone, the phenoxy and semiquinone radical of a-tocopherol (vitamin E), vitamin A D, and many others.
Chapter 6. Electron Paramagnetic Resonance Spectroscopy
6.1. Brief Basics of the Method
Electron paramagnetic resonance (EPR) spectroscopy is the phenomenon of resonant absorption of electromagnetic wave energy by paramagnetic particles placed in a constant magnetic field. This absorption occurs due to the fact that unpaired
the electrons of paramagnetic particles are oriented in a constant magnetic field so that their own angular momentum (spin) is directed either along the field or against the field. Absorption is a function of the unpaired electrons contained in
researched |
Due to |
takeovers |
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high-frequency field by the sample, an EPR signal appears. EPR spectrum |
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is the dependence of microwave energy absorption on |
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external |
magnetic |
Absorption of the beach |
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microwave magnetic field is recorded either on the screen |
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oscilloscope, or on the radio spectrometer recorder. |
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rice. 6.1 is given |
EPR spectrum |
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hypothetical connection.
radical. For these purposes, atlases of the EPR spectra of various compounds have been compiled. The following line parameters are important for interpreting EPR spectra: shape, intensity, position, and splitting.
It should be noted that the devices immediately give the first derivative of the energy absorption curve (Fig. 6.1).
The line intensity of an EPR spectrum is the area under its curve. It is proportional to the number of unpaired electrons in the sample. The position of the line in the EPR spectrum is taken to be the point at which the first
~O-CH-O~
Rice. 6.2. Scheme of the appearance of hyperfine splitting in the EPR spectrum of the median radical of polyformaldehyde
when the system |
contains nuclei with a magnetic moment, |
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for example, a proton (H1), near an unpaired electron, on a magnetic |
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The moment of an electron is affected by the orientation of the magnetic moment. kernels |
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as a result of such an interaction, each magnetic energy |
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electron |
splits |
SublevelsIt |
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the interaction of an electron and a magnetic nucleus is called hyperfine |
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interaction (STV), and |
split |
energy |
levels– |
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hyperfine splitting (Fig. 6.2). |
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6.2. Applications of EPR spectroscopy in |
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macromolecular chemistry |
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EPR spectroscopy |
macromolecular |
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is used to study free radicals generated in the following processes:
polymerization (photo-, radiation initiation, etc.);
· degradation of polymers;
· oxidation of polymers;
· splitting of macromolecules during mechanical destruction.
6.3. Study of the structure of radicals and molecular motions
The HFI energy of an unpaired electron with nuclei consists of two parts - isotropic and anisotropic. Thus, the isotropic part determines the energy of the dipole interaction of the electron with the nucleus, and it depends on the angle between the axis of the orbital of the unpaired electron and the direction of the constant magnetic field. Anisotropic HFI manifests itself in the EPR spectrum of radicals in solids, where the orientation of the radicals is rigidly fixed. Anisotropic HFI is absent in liquids.
polyethylene -CH 2 - CH - CH 2 - CH - (Fig. 6.3).
In a polycrystalline polymer, the spectrum consists of six lines
(Fig. 6.3, but). it |
due to the fact that |
interaction |
unpaired |
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electron |
carried out |
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magnetic equivalent |
protons |
constants |
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about the same. |
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Rice. 6.3. EPR spectra of the median radical of polyethylene in a polycrystal (a) and in a single crystal when the axis of the macromolecule is oriented along the field (b) and perpendicular to the field (c)
However, the spectrum of oriented polyethylene, in which the zigzag of the polymer chain is located along the direction of the field, already has five lines (Fig. 6.3, b). This EPR spectrum is due to the interaction of an unpaired electron with only four protons. The interaction with α-hydrogen in this orientation is small and does not show up in the spectrum.
If we now turn the field and direct it along the p-orbital, perpendicular to the zigzag of the chain, then 10 lines appear (Fig. 6.3, c). The doubling of the number of lines is due to the splitting on the α-proton, which is sufficiently large for this orientation.
Rice. 6.4. EPR spectra of the middle ~CH2 - CH - CH2 ~ (a) and terminal
~CH2 - C H2 (b ) polyethylene macroradicals
In polyethylene, the chains have a planar conformation, and therefore, in the middle radical, all five protons closest to the reaction center of the radical are magnetically equivalent. The EPR spectrum of such a radical (Fig. 6.4, a) consists of six lines, the intensity distribution of which is described by the binomial law. The EPR spectrum of the terminal radical consists of five lines (Fig. 6.4, b).
6.4. Study of chemical processes in polymers
The EPR method is used to detect radicals, study their transformations and radical reactions in polymers.
For research chemical processes it is important not only to identify radicals, but also to measure their concentrations. Direct determination of free radicals by EPR during free radical polymerization is currently not entirely successful. This is due to the fact that at conventional experimental polymerization rates, the concentration of radicals is very low.
Growing macroradicals in the liquid and solid phases were identified by EPR, their concentrations were determined, and the rate constants of chain growth and termination were found.