Electron paramagnetic resonance

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Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials with unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but it is electron spins that are excited instead of the spins of atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes or organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, [1] [2] and was developed independently at the same time by Brebis Bleaney at the University of Oxford.

Spectroscopy study of the interaction between matter and electromagnetic radiation

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of LIGO and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency.

Unpaired electron electron that occupies an orbital of an atom singly

In chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom has a capacity to contain two electrons with opposite spins. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively uncommon in chemistry, because an entity that carries an unpaired electron is usually rather reactive. In organic chemistry they typically only occur briefly during a reaction on an entity called a radical; however, they play an important role in explaining reaction pathways.

Nuclear magnetic resonance spectroscopic technique relying on the energy difference between the quantum spin states of electrons when exposed to an external magnetic field

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong static magnetic field are perturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics, crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI).

Contents

EPR spectrometer EPR spectometer.JPG
EPR spectrometer

Theory

Origin of an EPR signal

Every electron has a magnetic moment and spin quantum number , with magnetic components and . In the presence of an external magnetic field with strength , the electron's magnetic moment aligns itself either parallel () or antiparallel () to the field, each alignment having a specific energy due to the Zeeman effect:

Magnetic moment extensive physical property

The magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects.

Spin (physics) intrinsic form of angular momentum as a property of quantum particles

In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of electrons, the quantum numbers can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom". An important aspect of quantum mechanics is the quantization of the observable quantities, since quantum numbers are discrete sets of integers or half-integers, although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. An important family is flavour quantum numbers – internal quantum numbers which determine the type of a particle and its interactions with other particles through the forces. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.

where

A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or nucleus. It is essentially a proportionality constant that relates the observed magnetic moment μ of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.

In physics, the Landé g-factor is a particular example of a g-factor, namely for an electron with both spin and orbital angular momenta. It is named after Alfred Landé, who first described it in 1921.

In atomic physics, the Bohr magneton is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.

Therefore, the separation between the lower and the upper state is for unpaired free electrons. This equation implies (since both and are constant) that the splitting of the energy levels is directly proportional to the magnetic field's strength, as shown in the diagram below.

Magnetic field spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

Splitting of electron spin states EPR splitting.svg
Splitting of electron spin states

An unpaired electron can move between the two energy levels by either absorbing or emitting a photon of energy such that the resonance condition, , is obeyed. This leads to the fundamental equation of EPR spectroscopy: .

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and always moves at the speed of light within a vacuum.

Experimentally, this equation permits a large combination of frequency and magnetic field values, but the great majority of EPR measurements are made with microwaves in the 9000–10000 MHz (9–10 GHz) region, with fields corresponding to about 3500 G (0.35 T). Furthermore, EPR spectra can be generated by either varying the photon frequency incident on a sample while holding the magnetic field constant or doing the reverse. In practice, it is usually the frequency that is kept fixed. A collection of paramagnetic centers, such as free radicals, is exposed to microwaves at a fixed frequency. By increasing an external magnetic field, the gap between the and energy states is widened until it matches the energy of the microwaves, as represented by the double arrow in the diagram above. At this point the unpaired electrons can move between their two spin states. Since there typically are more electrons in the lower state, due to the Maxwell–Boltzmann distribution (see below), there is a net absorption of energy, and it is this absorption that is monitored and converted into a spectrum. The upper spectrum below is the simulated absorption for a system of free electrons in a varying magnetic field. The lower spectrum is the first derivative of the absorption spectrum. The latter is the most common way to record and publish continuous wave EPR spectra.

The gauss, abbreviated as G or Gs, is the cgs unit of measurement of magnetic flux density (B). It is named after German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter. The cgs system has been superseded by the International System of Units (SI), which uses the tesla as the unit of magnetic flux density. One gauss equals 1×104 tesla, so 1 tesla = 10,000 gauss.

The tesla is a derived unit of the magnetic induction in the International System of Units.

EPR lines.png

For the microwave frequency of 9388.2 MHz, the predicted resonance occurs at a magnetic field of about = 0.3350 teslas = 3350 gausses.

Because of electron-nuclear mass differences, the magnetic moment of an electron is substantially larger than the corresponding quantity for any nucleus, so that a much higher electromagnetic frequency is needed to bring about a spin resonance with an electron than with a nucleus, at identical magnetic field strengths. For example, for the field of 3350 G shown at the right, spin resonance occurs near 9388.2 MHz for an electron compared to only about 14.3 MHz for 1H nuclei. (For NMR spectroscopy, the corresponding resonance equation is where and depend on the nucleus under study.)

Field modulation

The field oscillates between B1 and B2 due to the superimposed modulation field at 100 kHz. This causes the absorption intensity to oscillate between I1 and I2. The larger the difference the larger the intensity detected by the detector tuned to 100 kHz (note this can be negative or even 0). As the difference between the two intensities is detected the first derivative of the absorption is detected. Field modulation diagram.jpg
The field oscillates between B1 and B2 due to the superimposed modulation field at 100 kHz. This causes the absorption intensity to oscillate between I1 and I2. The larger the difference the larger the intensity detected by the detector tuned to 100 kHz (note this can be negative or even 0). As the difference between the two intensities is detected the first derivative of the absorption is detected.

As previously mentioned an EPR spectrum is usually directly measured as the first derivative of the absorption. This is accomplished by using field modulation. A small additional oscillating magnetic field is applied to the external magnetic field at a typical frequency of 100 kHz. [4] By detecting the peak to peak amplitude the first derivative of the absorption is measured. By using phase sensitive detection only signals with the same modulation (100 kHz) are detected. This results in higher signal to noise ratios. Note field modulation is unique to continuous wave EPR measurements and spectra resulting from pulsed experiments are presented as absorption profiles.

Maxwell–Boltzmann distribution

In practice, EPR samples consist of collections of many paramagnetic species, and not single isolated paramagnetic centers. If the population of radicals is in thermodynamic equilibrium, its statistical distribution is described by the Maxwell–Boltzmann equation:

where is the number of paramagnetic centers occupying the upper energy state, is the Boltzmann constant, and is the thermodynamic temperature. At 298 K, X-band microwave frequencies ( ≈ 9.75 GHz) give ≈ 0.998, meaning that the upper energy level has a slightly smaller population than the lower one. Therefore, transitions from the lower to the higher level are more probable than the reverse, which is why there is a net absorption of energy.

The sensitivity of the EPR method (i.e., the minimal number of detectable spins ) depends on the photon frequency according to

where is a constant, is the sample's volume, is the unloaded quality factor of the microwave cavity (sample chamber), is the cavity filling coefficient, and is the microwave power in the spectrometer cavity. With and being constants, ~ , i.e., ~ , where ≈ 1.5. In practice, can change varying from 0.5 to 4.5 depending on spectrometer characteristics, resonance conditions, and sample size.

A great sensitivity is therefore obtained with a low detection limit and a large number of spins. Therefore, the required parameters are:

Spectral parameters

In real systems, electrons are normally not solitary, but are associated with one or more atoms. There are several important consequences of this:

  1. An unpaired electron can gain or lose angular momentum, which can change the value of its g-factor, causing it to differ from . This is especially significant for chemical systems with transition-metal ions.
  2. The magnetic moment of a nucleus with a non-zero nuclear spin will affect any unpaired electrons associated with that atom. This leads to the phenomenon of hyperfine coupling, analogous to J-coupling in NMR, splitting the EPR resonance signal into doublets, triplets and so forth.
  3. Interactions of an unpaired electron with its environment influence the shape of an EPR spectral line. Line shapes can yield information about, for example, rates of chemical reactions. [5]
  4. The g-factor and hyperfine coupling in an atom or molecule may not be the same for all orientations of an unpaired electron in an external magnetic field. This anisotropy depends upon the electronic structure of the atom or molecule (e.g., free radical) in question, and so can provide information about the atomic or molecular orbital containing the unpaired electron.

The g factor

Knowledge of the g-factor can give information about a paramagnetic center's electronic structure. An unpaired electron responds not only to a spectrometer's applied magnetic field but also to any local magnetic fields of atoms or molecules. The effective field experienced by an electron is thus written

where includes the effects of local fields ( can be positive or negative). Therefore, the resonance condition (above) is rewritten as follows:

The quantity is denoted and called simply the g-factor, so that the final resonance equation becomes

This last equation is used to determine in an EPR experiment by measuring the field and the frequency at which resonance occurs. If does not equal , the implication is that the ratio of the unpaired electron's spin magnetic moment to its angular momentum differs from the free-electron value. Since an electron's spin magnetic moment is constant (approximately the Bohr magneton), then the electron must have gained or lost angular momentum through spin–orbit coupling. Because the mechanisms of spin–orbit coupling are well understood, the magnitude of the change gives information about the nature of the atomic or molecular orbital containing the unpaired electron.

In general, the g factor is not a number but a second-rank tensor represented by 9 numbers arranged in a 3×3 matrix. The principal axes of this tensor are determined by the local fields, for example, by the local atomic arrangement around the unpaired spin in a solid or in a molecule. Choosing an appropriate coordinate system (say, x,y,z) allows one to "diagonalize" this tensor, thereby reducing the maximal number of its components from 9 to 3: gxx, gyy and gzz. For a single spin experiencing only Zeeman interaction with an external magnetic field, the position of the EPR resonance is given by the expression gxxBx + gyyBy + gzzBz. Here Bx, By and Bz are the components of the magnetic field vector in the coordinate system (x,y,z); their magnitudes change as the field is rotated, so does the frequency of the resonance. For a large ensemble of randomly oriented spins, the EPR spectrum consists of three peaks of characteristic shape at frequencies gxxB0, gyyB0 and gzzB0: the low-frequency peak is positive in first-derivative spectra, the high-frequency peak is negative, and the central peak is bipolar. Such situations are commonly observed in powders, and the spectra are therefore called "powder-pattern spectra". In crystals, the number of EPR lines is determined by the number of crystallographically equivalent orientations of the EPR spin (called "EPR center").

Hyperfine coupling

Since the source of an EPR spectrum is a change in an electron's spin state, the EPR spectrum for a radical (S = 1/2 system) would consist of one line. Greater complexity arises because the spin couples with nearby nuclear spins. The magnitude of the coupling is proportional to the magnetic moment of the coupled nuclei and depends on the mechanism of the coupling. Coupling is mediated by two processes, dipolar (through space) and isotropic (through bond).

This coupling introduces additional energy states and, in turn, multi-lined spectra. In such cases, the spacing between the EPR spectral lines indicates the degree of interaction between the unpaired electron and the perturbing nuclei. The hyperfine coupling constant of a nucleus is directly related to the spectral line spacing and, in the simplest cases, is essentially the spacing itself. [ citation needed ]

Two common mechanisms by which electrons and nuclei interact are the Fermi contact interaction and by dipolar interaction. The former applies largely to the case of isotropic interactions (independent of sample orientation in a magnetic field) and the latter to the case of anisotropic interactions (spectra dependent on sample orientation in a magnetic field). Spin polarization is a third mechanism for interactions between an unpaired electron and a nuclear spin, being especially important for -electron organic radicals, such as the benzene radical anion. The symbols "a" or "A" are used for isotropic hyperfine coupling constants, while "B" is usually employed for anisotropic hyperfine coupling constants. [6]

In many cases, the isotropic hyperfine splitting pattern for a radical freely tumbling in a solution (isotropic system) can be predicted.

Multiplicity

  • For a radical having M equivalent nuclei, each with a spin of I, the number of EPR lines expected is 2MI + 1. As an example, the methyl radical, CH3, has three 1H nuclei, each with I = 1/2, and so the number of lines expected is 2MI + 1 = 2(3)(1/2) + 1 = 4, which is as observed.
  • For a radical having M1 equivalent nuclei, each with a spin of I1, and a group of M2 equivalent nuclei, each with a spin of I2, the number of lines expected is (2M1I1 + 1) (2M2I2 + 1). As an example, the methoxymethyl radical, H2C(OCH3), has two equivalent 1H nuclei, each with I = 1/2 and three equivalent 1H nuclei each with I = 1/2, and so the number of lines expected is (2M1I1 + 1) (2M2I2 + 1) = [2(2)(1/2) + 1] [2(3)(1/2) + 1] = 3×4 = 12, again as observed.
Simulated EPR spectrum of the CH3 radical EPR methyl.png
Simulated EPR spectrum of the CH3 radical
  • The above can be extended to predict the number of lines for any number of nuclei.

While it is easy to predict the number of lines, the reverse problem, unraveling a complex multi-line EPR spectrum and assigning the various spacings to specific nuclei, is more difficult.

In the often encountered case of I = 1/2 nuclei (e.g., 1H, 19F, 31P), the line intensities produced by a population of radicals, each possessing M equivalent nuclei, will follow Pascal's triangle. For example, the spectrum at the right shows that the three 1H nuclei of the CH3 radical give rise to 2MI + 1 = 2(3)(1/2) + 1 = 4 lines with a 1:3:3:1 ratio. The line spacing gives a hyperfine coupling constant of aH = 23 G for each of the three 1H nuclei. Note again that the lines in this spectrum are first derivatives of absorptions.

Simulated EPR spectrum of the H2C(OCH3) radical EPR methoxymethyl.png
Simulated EPR spectrum of the H2C(OCH3) radical

As a second example, the methoxymethyl radical, H3COCH2. the OCH2 center will give an overall 1:2:1 EPR pattern, each component of which is further split by the three methoxy hydrogens into a 1:3:3:1 pattern to give a total of 3×4 = 12 lines, a triplet of quartets. A simulation of the observed EPR spectrum is shown at the right and agrees with the 12-line prediction and the expected line intensities. Note that the smaller coupling constant (smaller line spacing) is due to the three methoxy hydrogens, while the larger coupling constant (line spacing) is from the two hydrogens bonded directly to the carbon atom bearing the unpaired electron. It is often the case that coupling constants decrease in size with distance from a radical's unpaired electron, but there are some notable exceptions, such as the ethyl radical (CH2CH3).

Resonance linewidth definition

Resonance linewidths are defined in terms of the magnetic induction B and its corresponding units, and are measured along the x axis of an EPR spectrum, from a line's center to a chosen reference point of the line. These defined widths are called halfwidths and possess some advantages: for asymmetric lines, values of left and right halfwidth can be given. The halfwidth is the distance measured from the line's center to the point in which absorption value has half of maximal absorption value in the center of resonance line. First inclination width is a distance from center of the line to the point of maximal absorption curve inclination. In practice, a full definition of linewidth is used. For symmetric lines, halfwidth , and full inclination width .


Applications

EPR/ESR spectroscopy is used in various branches of science, such as biology, chemistry and physics, for the detection and identification of free radicals and paramagnetic centers such as F-centers. EPR is a sensitive, specific method for studying both radicals formed in chemical reactions and the reactions themselves. For example, when ice (solid H2O) is decomposed by exposure to high-energy radiation, radicals such as H, OH, and HO2 are produced. Such radicals can be identified and studied by EPR. Organic and inorganic radicals can be detected in electrochemical systems and in materials exposed to UV light. In many cases, the reactions to make the radicals and the subsequent reactions of the radicals are of interest, while in other cases EPR is used to provide information on a radical's geometry and the orbital of the unpaired electron. EPR/ESR spectroscopy is also used in geology and archaeology as a dating tool. It can be applied to a wide range of materials such as carbonates, sulfates, phosphates, silica or other silicates. [7]

Medical and biological applications of EPR also exist. Although radicals are very reactive, and so do not normally occur in high concentrations in biology, special reagents have been developed to spin-label molecules of interest. These reagents are particularly useful in biological systems. Specially-designed nonreactive radical molecules can attach to specific sites in a biological cell, and EPR spectra can then give information on the environment of these so-called spin labels or spin probes. Spin-labeled fatty acids have been extensively used to study dynamic organisation of lipids in biological membranes, [8] lipid-protein interactions [9] and temperature of transition of gel to liquid crystalline phases. [10]

A type of dosimetry system has been designed for reference standards and routine use in medicine, based on EPR signals of radicals from irradiated polycrystalline α-alanine (the alanine deamination radical, the hydrogen abstraction radical, and the (CO(OH))=C(CH3)NH2+ radical) . This method is suitable for measuring gamma and x-rays, electrons, protons, and high-linear energy transfer (LET) radiation of doses in the 1 Gy to 100 kGy range. [11]

EPR/ESR spectroscopy can be applied only to systems in which the balance between radical decay and radical formation keeps the free radicals concentration above the detection limit of the spectrometer used. This can be a particularly severe problem in studying reactions in liquids. An alternative approach is to slow down reactions by studying samples held at cryogenic temperatures, such as 77 K (liquid nitrogen) or 4.2 K (liquid helium). An example of this work is the study of radical reactions in single crystals of amino acids exposed to x-rays, work that sometimes leads to activation energies and rate constants for radical reactions.

The study of radiation-induced free radicals in biological substances (for cancer research) poses the additional problem that tissue contains water, and water (due to its electric dipole moment) has a strong absorption band in the microwave region used in EPR spectrometers.[ citation needed ]

EPR/ESR also has been used by archaeologists for the dating of teeth. Radiation damage over long periods of time creates free radicals in tooth enamel, which can then be examined by EPR and, after proper calibration, dated. Alternatively, material extracted from the teeth of people during dental procedures can be used to quantify their cumulative exposure to ionizing radiation. People exposed to radiation from the Chernobyl disaster have been examined by this method. [12] [13]

Radiation-sterilized foods have been examined with EPR spectroscopy, the aim being to develop methods to determine whether a particular food sample has been irradiated and to what dose. [ citation needed ]

EPR/ESR spectroscopy has been used to measure properties of crude oil, in particular asphaltene and vanadium content. EPR measurement of asphaltene content is a function of spin density and solvent polarity. Prior work dating to the 1960s has demonstrated the ability to measure vanadium content to sub-ppm levels.[ citation needed ]

In the field of quantum computing, pulsed EPR is used to control the state of electron spin qubits in materials such as diamond, silicon and gallium arsenide.[ citation needed ]

High-field high-frequency measurements

High-field high-frequency EPR measurements are sometimes needed to detect subtle spectroscopic details. However, for many years the use of electromagnets to produce the needed fields above 1.5 T was impossible, due principally to limitations of traditional magnet materials. The first multifunctional millimeter EPR spectrometer with a superconducting solenoid was described in the early 1970s by Prof. Y. S. Lebedev's group (Russian Institute of Chemical Physics, Moscow) in collaboration with L. G. Oranski's group (Ukrainian Physics and Technics Institute, Donetsk), which began working in the Institute of Problems of Chemical Physics, Chernogolovka around 1975. [14] Two decades later, a W-band EPR spectrometer was produced as a small commercial line by the German Bruker Company, initiating the expansion of W-band EPR techniques into medium-sized academic laboratories.

WavebandLSCXPKQUVEWFDJ
30010075302012.58.564.643.22.72.11.61.10.83
1341015243550657595111140190285360
0.030.110.140.330.540.861.251.82.32.73.53.94.96.810.212.8

The EPR waveband is stipulated by the frequency or wavelength of a spectrometer's microwave source (see Table).

EPR experiments often are conducted at X and, less commonly, Q bands, mainly due to the ready availability of the necessary microwave components (which originally were developed for radar applications). A second reason for widespread X and Q band measurements is that electromagnets can reliably generate fields up to about 1 tesla. However, the low spectral resolution over g-factor at these wavebands limits the study of paramagnetic centers with comparatively low anisotropic magnetic parameters. Measurements at > 40 GHz, in the millimeter wavelength region, offer the following advantages:

EPR spectra of TEMPO, a nitroxide radical, as a function of frequency. Note the improvement in resolution from left to right. EPR multifrequency spectra.png
EPR spectra of TEMPO, a nitroxide radical, as a function of frequency. Note the improvement in resolution from left to right.
  1. EPR spectra are simplified due to the reduction of second-order effects at high fields.
  2. Increase in orientation selectivity and sensitivity in the investigation of disordered systems.
  3. The informativity and precision of pulse methods, e.g., ENDOR also increase at high magnetic fields.
  4. Accessibility of spin systems with larger zero-field splitting due to the larger microwave quantum energy h.
  5. The higher spectral resolution over g-factor, which increases with irradiation frequency and external magnetic field B0. This is used to investigate the structure, polarity, and dynamics of radical microenvironments in spin-modified organic and biological systems through the spin label and probe method. The figure shows how spectral resolution improves with increasing frequency.
  6. Saturation of paramagnetic centers occurs at a comparatively low microwave polarizing field B1, due to the exponential dependence of the number of excited spins on the radiation frequency . This effect can be successfully used to study the relaxation and dynamics of paramagnetic centers as well as of superslow motion in the systems under study.
  7. The cross-relaxation of paramagnetic centers decreases dramatically at high magnetic fields, making it easier to obtain more-precise and more-complete information about the system under study. [14]

This was demonstrated experimentally in the study of various biological, polymeric and model systems at D-band EPR. [15]

Hardware components

The microwave bridge

The microwave bridge contains both the microwave source and the detector. [16] Older spectrometers used a vacuum tube called a klystron to generate microwaves, but modern spectrometers use a Gunn diode. Immediately after the microwave source there is an isolator which serves to attenuate any reflections back to the source which would result in fluctuations in the microwave frequency. [17] The microwave power from the source is then passed through a directional coupler which splits the microwave power into two paths, one directed towards the cavity and the other the reference arm. Along both paths there is a variable attenuator that facilitates the precise control of the flow of microwave power. This in turn allows for accurate control over the intensity of the microwaves subjected to the sample. On the reference arm, after the variable attenuator there is a phase shifter that sets a defined phase relationship between the reference and reflected signal which permits phase sensitive detection.

Most EPR machines are reflection spectrometers, meaning that the detector should only be exposed to microwave radiation coming back from the cavity. This is achieved by the use of a device known as the circulator which directs the microwave radiation (from the branch that is heading towards the cavity) into the cavity. Reflected microwave radiation (after absorption by the sample) is then passed through the circulator towards the detector, ensuring it does not go back to the microwave source. The reference signal and reflected signal are combined and passed to the detector diode which converts the microwave power into an electrical current.

The need for the reference arm

At low energies (less than 1 μW) the diode current is proportional to the microwave power and the detector is referred to as a square-law detector. At higher power levels (greater than 1 mW) the diode current is proportional to the square root of the microwave power and the detector is called a linear detector. In order to obtain optimal sensitivity as well as quantitative information the diode should be operating within the linear region. To ensure the detector is operating at that level the reference arm serves to provide a "bias".

The magnet

In an EPR machine the magnetic assembly includes the magnetic with a dedicated power supply as well as a field sensor or regulator such as a Hall probe. EPR machines use one of two types of magnet which is determined by the operating microwave frequency (which determine the range of magnetic field strengths required). The first is an electromagnet which are generally capable of generating field strengths of up to 1.5 T making them suitable for measurements using the Q-band frequency. In order to generate field strengths appropriate for W-band and higher frequency operation superconducting magnets are employed. The magnetic field is homogeneous across the sample volume and has a high stability at static field.

The microwave resonator (cavity)

The microwave resonator is designed to enhance the microwave magnetic field at the sample in order to induce EPR transitions. It is a metal box with a rectangular or cylindrical shape that resonates with microwaves (like an organ pipe with sound waves). At the resonance frequency of the cavity microwaves remain inside the cavity and are not reflected back. Resonance means the cavity stores microwave energy and its ability to do this is given by the quality factor (Q), defined by the following equation:

The higher the value of Q the higher the sensitivity of the spectrometer. The energy dissipated is the energy lost in one microwave period. Energy may be lost to the side walls of the cavity as microwaves may generate currents which in turn generate heat. A consequence of resonance is the creation of a standing wave inside the cavity. Electromagnetic standing waves have their electric and magnetic field components exactly out of phase. This provides an advantage as the electric field provides nonresonant absorption of the microwaves, which in turn increases the dissipated energy and reduces Q. To achieve the largest signals and hence sensitivity the sample is positioned such that it lies within the magnetic field maximum and the electric field minimum. When the magnetic field strength is such that an absorption event occurs, the value of Q will be reduced due to the extra energy loss. This results in a change of impedance which serves to stop the cavity from being critically coupled. This means microwaves will now be reflected back to the detector (in the microwave bridge) where an EPR signal is detected. [18]

Pulsed electron paramagnetic resonance

The dynamics of electron spins are best studied with pulsed measurements. [19] Microwave pulses typically 10–100 ns long are used to control the spins in the Bloch sphere. The spin–lattice relaxation time can be measured with an inversion recovery experiment.

As with pulsed NMR, the Hahn echo is central to many pulsed EPR experiments. A Hahn echo decay experiment can be used to measure the dephasing time, as shown in the animation below. The size of the echo is recorded for different spacings of the two pulses. This reveals the decoherence, which is not refocused by the pulse. In simple cases, an exponential decay is measured, which is described by the time.

GWM HahnEchoDecay.gif

Pulsed electron paramagnetic resonance could be advanced into electron nuclear double resonance spectroscopy (ENDOR), which utilizes waves in the radio frequencies. Since different nuclei with unpaired electrons respond to different wavelengths, radio frequencies are required at times. Since the results of the ENDOR gives the coupling resonance between the nuclei and the unpaired electron, the relationship between them can be determined.

See also

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In atomic physics, hyperfine structure refers to small shifts and splittings in the energy levels of atoms, molecules, and ions, due to interaction between the state of the nucleus and the state of the electron clouds.

Nuclear quadrupole resonance spectroscopy or NQR is a chemical analysis technique related to nuclear magnetic resonance (NMR). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a magnetic field, and for this reason NQR spectroscopy is referred to as "zero Field NMR." The NQR resonance is mediated by the interaction of the electric field gradient (EFG) with the quadrupole moment of the nuclear charge distribution. Because the EFG at the location of a nucleus in a given substance is determined primarily by the valence electrons involved in the particular bond with other nearby nuclei, the NQR frequency at which transitions occur is unique for a given substance. A particular NQR frequency in a compound or crystal is proportional to the product of the nuclear quadrupole moment, a property of the nucleus, and the EFG in the neighborhood of the nucleus. It is this product which is termed the nuclear quadrupole coupling constant for a given isotope in a material and can be found in tables of known NQR transitions.

Dynamic nuclear polarization (DNP) results from transferring spin polarization from electrons to nuclei, thereby aligning the nuclear spins to the extent that electron spins are aligned. Note that the alignment of electron spins at a given magnetic field and temperature is described by the Boltzmann distribution under the thermal equilibrium. It is also possible that those electrons are aligned to a higher degree of order by other preparations of electron spin order such as: chemical reactions, optical pumping and spin injection. DNP is considered one of several techniques for hyperpolarization. DNP can also be induced using unpaired electrons produced by radiation damage in solids.

In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy.

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is approximately −9.284764×10−24 J/T. The electron magnetic moment has been measured to an accuracy of 7.6 parts in 1013.

Solid-state nuclear magnetic resonance

Solid-state NMR (SSNMR) spectroscopy is a kind of nuclear magnetic resonance (NMR) spectroscopy, characterized by the presence of anisotropic interactions.

Larmor precession

In physics, Larmor precession is the precession of the magnetic moment of an object about an external magnetic field. Objects with a magnetic moment also have angular momentum and effective internal electric current proportional to their angular momentum; these include electrons, protons, other fermions, many atomic and nuclear systems, as well as classical macroscopic systems. The external magnetic field exerts a torque on the magnetic moment,

Ferromagnetic resonance, or FMR, is a spectroscopic technique to probe the magnetization of ferromagnetic materials. It is a standard tool for probing spin waves and spin dynamics. FMR is very broadly similar to electron paramagnetic resonance (EPR), and also somewhat similar to nuclear magnetic resonance (NMR), except that FMR probes the sample magnetization resulting from the magnetic moments of dipolar-coupled but unpaired electrons, while NMR probes the magnetic moment of atomic nuclei that are screened by the atomic or molecular orbitals surrounding such nuclei of non-zero nuclear spin.

Nitrogen-vacancy center Point defect in diamonds

A nitrogen-vacancy center is one of numerous point defects in diamond. Its most explored and useful property is photoluminescence, which can be easily detected from an individual N-V center, especially those in the negative charge state (N-V). Electron spins at N-V centers, localized at atomic scales, can be manipulated at room temperature by applying a magnetic field, electric field, microwave radiation or light, or a combination, resulting in sharp resonances in the intensity and wavelength of the photoluminescence. These resonances can be explained in terms of electron spin related phenomena such as quantum entanglement, spin-orbit interaction and Rabi oscillations, and analysed using advanced quantum optics theory. An individual N-V center can be viewed as a basic unit of a quantum computer, and it has potential applications in novel, more efficient fields of electronics and computational science including quantum cryptography, spintronics and masers.

DPPH chemical compound

DPPH is a common abbreviation for the organic chemical compound 2,2-diphenyl-1-picrylhydrazyl. It is a dark-colored crystalline powder composed of stable free-radical molecules. DPPH has two major applications, both in laboratory research: one is a monitor of chemical reactions involving radicals, most notably it is a common antioxidant assay, and another is a standard of the position and intensity of electron paramagnetic resonance signals.

Electron nuclear double resonance (ENDOR) is a magnetic resonance technique for elucidating the molecular and electronic structure of paramagnetic species. The technique was first introduced to resolve interactions in electron paramagnetic resonance (EPR) spectra. It is currently practiced in a variety of modalities, mainly in the areas of biophysics and heterogeneous catalysis.

Acoustic paramagnetic resonance (APR) is a phenomenon of resonant absorption of sound by a system of magnetic particles placed in an external magnetic field. It occurs when the energy of the sound wave quantum becomes equal to the splitting of the energy levels of the particles, the splitting being induced by the magnetic field. APR is a variation of electron paramagnetic resonance (EPR) where the acoustic rather than electromagnetic waves are absorbed by the studied sample. APR was theoretically predicted in 1952, independently by Semen Altshuler and Alfred Kastler, and was experimentally observed by W. G. Proctor and W. H. Tanttila in 1955.

Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpaired electrons. Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μeff. For first-row transition metals the magnitude of μeff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin-orbit coupling causes μeff to deviate from the spin-only formula. For the heavier transition metals, lanthanides and actinides, spin-orbit coupling cannot be ignored. Exchange interaction can occur in clusters and infinite lattices, resulting in ferromagnetism, antiferromagnetism or ferrimagnetism depending on the relative orientations of the individual spins.

Pulsed electron paramagnetic resonance

Pulsed electron paramagnetic resonance (EPR) is an electron paramagnetic resonance technique that involves the alignment of the net magnetization vector of the electron spins in a constant magnetic field. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. Fourier transformation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo envelope modulation (ESEEM) or pulsed electron nuclear double resonance (ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins.

Electric dipole spin resonance (EDSR) is a method to control the magnetic moments inside a material using quantum mechanical effects like the spin–orbit interaction. Mainly, EDSR allows to flip the orientation of the magnetic moments through the use of electromagnetic radiation at resonant frequencies. EDSR was first proposed by Emmanuel Rashba.

In physics, Optically Detected Magnetic Resonance (ODMR) is a double resonance technique by which the electron spin state of a crystal defect may be optically pumped for spin initialisation and readout.

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