Electronic paramagnetic resonance

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RPE Spectrometer

Electronic paramagnetic resonance (RPE or EPR) or electron spin resonance (REE) is a spectroscopic technique sensitive to unpaired electrons. Generally, it is a free radical for organic molecules or a transition metal ion if it is an inorganic compound. Since most stable molecules have a closed-shell configuration, with all spins paired, this technique has less application than nuclear magnetic resonance (NMR). Electron paramagnetic resonance was first observed at Kazan Federal University by Soviet physicist Yevgeny Zavoiski in 1944, and was developed independently at the same time by Brebis Bleaney at Oxford University.

The physical principles of this technique are analogous to those of NMR, but in the case of RPE, electronic spins are excited instead of nuclear ones. The energy of interaction with the magnetic field of electrons is much higher than that of nuclei, so weaker external magnetic fields and higher electromagnetic frequencies are used. In a 0.3 T magnetic field, RPE occurs around 10 GHz.

RPE is used in solid-state physics to identify and quantify radicals (ie, molecules with unpaired electrons), as well as in biology and medicine to track biological spin probes. These probes are molecules with unpaired electrons specially designed to stabilize these electrons and attach to specific sites in a cell, so that information can be obtained from this site by measuring the environment of these electrons.

To detect some subtle details in some systems, high-frequency, high-field RPE is needed. Unlike ordinary RPE, which is affordable for university laboratories, there are few centers in the world that offer high-field, high-frequency RPE. Among them are the ILL in Grenoble (France) and another in Tallahassee (United States of America).

Theory

Origin of an RPE signal

Each electron has a magnetic moment and a quantum spin number ${displaystyle s={frac {1}{2}}}$ with magnetic components ${displaystyle m_{s}=+{frac {1}{2}}}$ or ${displaystyle m_{s}=-{frac {1}{2}}}$ . In the presence of an external magnetic field of strength ${displaystyle B_{0}}$ , the magnetic moment of the electron aligns with the field in anti-parallel form (if ${displaystyle m_{s}=-{frac {1}{2}}}$ or parallel (if ${displaystyle m_{s}=+{frac {1}{2}}}$ ). Each alignment has a specific energy due to the Zeeman effect, described by the equation:

${displaystyle E=m_{s}g_{e}mu _{B}B_{0}}$

Where:

$E$ is the specific energy of alignment

${displaystyle g_{e}}$ is the electron factor g (see also the Landé factor), with a value of ${displaystyle g_{e}=2.0023}$ for a free electron. It is a dimensional value because it represents the relationship between the magnetic moment of a particle and its angular number.
${displaystyle mu _{B}}$ It's Bohr's magnet.
${displaystyle B_{0}}$ is the magnetic field and
${displaystyle m_{s}}$ It's the thorn.

Therefore, the separation between the lowest and the highest energy state corresponds to ${displaystyle Delta E=g_{e}mu _{B}B_{0}}$ for free electrons without matching. Because both the g factor of the electron and the Bohr magneton are constant, the equation implies that the separation of energy levels is directly proportional to the force of the magnetic field as shown in the diagram below.

In the axis of the abscises the value of the magnetic field and in the of the ordered ones, the specific energy of the alignment.

A missing electron can move between both energy levels either by absorbing or emitting an energy photon ${displaystyle hnu }$ so that the resonance condition ${displaystyle hnu =Delta E}$ It's done. This results in the fundamental equation of RPE spectroscopy: ${displaystyle hnu =g_{e}mu _{B}B_{0}}$ .

Experimentally, this equation allows for a wide combination of frequencies and magnetic field values, but the vast majority of RPE measurements are made with microwaves in the region of 9,000 to 10,000 MHz (9-10 GHz), with corresponding fields around 3500 G (0.35 T). Then, RPE spectra can be generated either by varying the frequency of the incident photon on the sample and keeping the magnetic field constant, or, conversely, by varying the magnetic field and keeping the photon frequency constant. In practice, it is usually the frequency of the photon that remains fixed.

If a group of paramagnetic centers, for example free radicals, is exposed to microwave at a fixed frequency, by increasing the external magnetic field, the energy gap between the energy states ${displaystyle m_{s}=+{frac {1}{2}}}$ and ${displaystyle m_{s}=-{frac {1}{2}}}$ is enlarged until the microwave energy equals (represented by the double arrow in the above diagram). At this point, uneven electrons can move between both states of the spine. Because there are usually more electrons in the lower state due to the distribution of Maxwell-Boltzmann, there is a net absorption of energy and it is this absorption that is monitored and converted into a spectrum. The upper spectrum in the image below is the simulated absorption for a free electron system in a variable magnetic field. The lower spectrum is the first derivative of the absorption spectrum. The latter is the most common way to represent and publish RPE spectra.

In the axis of abscises: Magnetic field strength in Gauss. On the axis of the orders: Sign received by the team. The above signal is the energy absorbance and the bottom is its first derivative.

In this case, for a microwave frequency 9388.2 MHz, the predicted resonance occurs at a magnetic field value of about 3350 G or 0.3350 T, calculated using the equation ${displaystyle B_{0}={frac {hnu }{g_{e}mu _{B}}}}$

Due to the mass differences between the electron and the nucleus, the magnetic moment of an electron is significantly greater than the corresponding amount for any nucleus, so a higher electromagnetic frequency is required to carry out a spin resonance than that required for a nucleus at similar magnetic field values. For example, for a 3350 G field, like the one shown above, electron spin resonance occurs near 9388.2 MHz while for a nucleus of ¹H, only 14.3 MHz are required.

Field modulation

The field ranges between B₁ and B₂ due to the overlay of the field at 100 kHz. This causes the absorption intensity to oscillate between I₁ and I₂. The greater the difference, the greater the detected intensity. As a difference between intensity is detected, the first derivative of absorption is detected.

As mentioned above, an RPE spectrum is usually measured directly as the first derivative of absorbance. This is achieved by a modulation of the field. A small additional oscillating magnetic field is applied to the external magnetic field at a typical frequency of 100 kilohertz. By detecting the amplitude between wave peaks, the first derivative of absorption can be measured. When using phase sensitive detection, only signals of the same modulation (100 kHz) are detected. This results in high signal to noise ratios. Field modulation is unique to continuous wave RPE measurements and the resulting spectra from such experiments are presented as absorption profiles.

Maxwell–Boltzmann distribution

In practice, RPE samples consist of groups of various paramagnetic species and not just isolated paramagnetic centers. If the population of radicals is in thermodynamic equilibrium, its statistical distribution is described by the Maxwell-Boltzmann equation:

${displaystyle {frac {n_{text{sup}}}{n_{text{inf}}}}=e^{-{frac {E_{text{sup}}-E_{text{inf}}}{kT}}}=e^{-{frac {Delta E}{kT}}}=e^{-{frac {epsilon }{kT}}}=e^{-{frac {hnu }{kT}}}}$

where ${displaystyle n_{text{sup}}}$ is the number of paramagnetic centers that occupy the state of higher energy, $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature, expressed in Kelvin. A 298 K, X-band microwave frequencies ( ${displaystyle nu approx 9.75 GHz}$ ) give a relationship ${displaystyle {frac {n_{text{sup}}}{n_{text{inf}}}}approx 0.998}$ , which means that the higher level of energy has a population slightly lower than that of the lower level. Therefore, transitions from lower to higher status are more likely than the opposite, which explains why there is a net absorption of energy.

The sensitivity of the RPE method (the minimum number of detectable spins ${displaystyle N_{text{min}}}$ ) depends on the frequency of the photon $nu$ according to the equation:

${displaystyle N_{text{min}}={frac {k_{1}V}{Q_{0}k_{f}v^{2}P^{text{1/2}}}}}$

Where:

$k_{1}$ It's a constant,

$V$ is the volume of the sample

$Q_0$ is the quality factor of the microwave chamber

${displaystyle k_{f}}$ is the filling coefficient of the camera and

$P$ is the microwave power in the spectrometer chamber.

With ${displaystyle k_{f}}$ and $P$ being constant, ${displaystyle N_{text{min}}thicksim (Q_{0}nu ^{2})^{text{-1}}}$ for example, ${displaystyle N_{text{min}}thicksim nu ^{-alpha }}$ where ${displaystyle alpha approx 1.5}$ . In practice, $alpha$ can vary from 0.5 to 4.5 depending on the spectrometer characteristics, resonance conditions and sample size.

A great sensitivity can be achieved with a low detection limit ${displaystyle N_{text{min}}}$ and a large number of spins. So, the required parameters are:

A high frequency of spectrometer to maximize equation 2.
A low temperature to decrease the number of spikes at the upper level of energy. This conditions explains why spectra are usually performed at the boiling temperature of the liquid nitrogen or the liquid helium.

Spectral parameters

In real systems, electrons are not normally found in isolation, but rather are associated with one or more atoms. There are several important consequences to this:

A missing electron can gain or lose angular momentum, which changes the value of its factor g, which causes it to differ from ${displaystyle g_{e}}$ . This is particularly important in chemical systems that have transition metal ions.
Systems with multiple uncoupled electrons can experience inter-electronic interactions that give rise to the “smooth structure”. This is noted in the null field and exchange interactions and may have a fairly large magnitude.
The magnetic moment of a nucleus with a different nuclear spine of zero will affect any uneven electron associated with that atom. This leads to the hyperfinal coupling phenomenon, similar to the J coupling in nuclear magnetic resonance, which corresponds to the dedoblation in doubles, triplets and others. Minor additional depopulations caused by nearby nuclei are usually called "superhyperphin" couplings.
Interactions of an electron disconnected with their environment modify the form of a spectrum of RPE. The form of spectra can provide information about, for example, advances in chemical reactions.
These effects (factor g, hyperfinal coupling, null field depopulation, exchange interactions) in an atom or molecule can be different for all orientations of an electron disconnected in an external magnetic field. This anisotropy depends on the electronic structure of the atom or molecule in question and may provide information about the atomic or molecular orbital that contains the electron disassociated.

The g-factor

Knowing factor g can provide information about the electronic structure of a paramagnetic center. A missing electron responds not only to the applied magnetic field of spectrometer ${displaystyle B_{0}}$ , but also to any local magnetic field of atoms and molecules. The effective magnetic field ${displaystyle B_{eff}}$ that experiences an electron is then written as follows:

${displaystyle B_{eff}=B_{0}(1-sigma)}$

where ${displaystyle sigma }$ is a correction factor that includes the effects of local fields ( $sigma$ can be positive or negative). Therefore, resonance condition ${displaystyle hnu =g_{e}mu _{B}B_{eff}}$ is rewritten as follows:

${displaystyle hnu =g_{e}mu _{B}B_{eff}=g_{e}mu _{B}B_{0}(1-sigma)}$

if the terms are grouped, the amount ${displaystyle g_{e}(1-sigma)}$ can simply be called $g$ and also receives the name factor-g, so the final resonance equation becomes:

${displaystyle hnu =gmu _{B}B_{0}}$

This last equation is used to determine $g$ in an RPE experiment, measuring the field and frequency to which the resonance occurs. Yeah. ${displaystyle gneq g_{e}}$ , it is implied that the relationship of the magnetic spin moment of the electrons disconnected with respect to the angular moment differs from the value for a free electron. Because the magnetic moment of spin of an electron is constant (approximately the value of the Bohr magneton), it can be deduced that the electron must have gained or lost angular momentum through the spinal-orbit coupling.Because the mechanisms of the spinal-orbit coupling are well studied, the magnitude of the change provides information about the nature of the atomic or molecular orbital that contains.

In general, the g factor is not a scale quantity but a two-order tensor, represented by 9 numbers ordered in a 3x3 matrix. The main axes of this tensor are determined by the local fields, for example, by the local atomic arrangement around the spawning in a solid or molecule. The proper choice of a coordinate system (such as x, and z), allows the tensor to "diagonalize", thus reducing the maximum number of components from 9 to 3: ${displaystyle g_{xx},g_{yy}}$ and ${displaystyle g_{zz}}$ . For a single spin that experiences only the Zeeman interaction with an external magnetic field, the position of the RPE resonance is given by the expression ${displaystyle g_{xx}B_{x}+g_{yy}B_{y}+g_{zz}B_{z}}$ . In this expression, ${displaystyle B_{x},B_{y},B_{z}}$ are magnetic field vector components in a coordinate system (x,y,z) and their numbers change according to the magnetic field is rotated, as well as the resonance frequency changes. For a large group of spins randomly oriented, the RPE spectrum consists of three peaks characteristically to frequencies ${displaystyle g_{xx}B_{0},g_{yy}B_{0} y g_{zz}B_{0}}$ : The low frequency peak is positive in the spectrum of the first derivative, the high frequency is negative and the central peak is bipolar. Such situations are commonly observed in dust and the spectrum then receives the name of "dust pattern specter". In crystals, the number of RPE lines is determined by the number of crystallographic orientations equivalent to RPE (RPE center).

Hyperfine coupling

Since the origin of an RPE spectrum is the change in the state of an electron spin, the RPE spectrum for a radical (system with S=1/2) should consist of a single line. Further complexity arises from the fact that the electron spin couples with nearby nuclear spins. The magnitude of this coupling is proportional to the magnetic moment of the coupled nucleus and depends on the coupling mechanism. Coupling is mediated by two processes: dipolar (through space) and isotropic (through a bond).

This coupling introduces additional energy states and consequently produces spectra with various lines. In these cases, the spacing between the RPE spectral lines indicates the degree of interaction between the unpaired electrons and the disturbing nucleus. The hyperfine coupling constant of a nucleus is directly related to the spacing between the spectral lines and, in the simplest cases, is essentially the spacing itself.

Two common mechanisms by which electrons and the nucleus interact are the Fermi contact interaction and the dipole interaction. The first applies broadly to the case of isotropic interactions (independent of the orientation of the sample in a magnetic field) and the second applies to the case of anisotropic interactions (spectra dependent on the orientation of the sample in a magnetic field). Spin polarization is the third mechanism for interactions between an unpaired electron and nuclear spin, being especially important for organic radicals possessing π electrons, such as the radical anion benzene. The symbols "a" and "A" are used to represent the isotropic hyperfine coupling constants, while "B" it is usually used for anisotropic hyperfine coupling constants. Strictly, a refers to the hyperfine doubling constant, a spacing between lines measured in units of magnetic field, while A and B refer to hyperfine coupling constants which are measured in units of frequency. The splitting and coupling constants are proportional, but they are not identical.

In most cases, isotropic hyperfine cleavage patterns for a radical moving freely in solution (isotropic system) can be predicted.

Multiplicity

For a radical that possesses a quantity M of equivalent cores, each with a spin l, the number of lines expected in the RPE spectrum is ${displaystyle 2Ml+1}$ . For example, the radical methyl ${displaystyle {ce {CH3{.}}}}$ possesses three cores of ¹H, each with ${displaystyle l=1/2}$ , so the number of lines expected is ${displaystyle 2Ml+1=2(3)(1/2)+1=4}$ as shown in experimental results.

RPE Spectrum for the Radical Method
For a radical he possesses M₁ equivalent cores, each with a spin I₁ and another group M₂ equivalent cores with spin I₂ the number of lines expected is ${displaystyle (2M_{1}I_{1}+1)(2M_{2}I_{2}+1)}$ . For example, the radical metoxymethyl ${displaystyle {ce {H3C(OCH2){.}}}}$ has a group of two equivalent cores ${displaystyle {ce {^1H}}}$ each with ${displaystyle l=1/2}$ and another group of three equivalent cores ${displaystyle {ce {^1H}}}$ with a thorn ${displaystyle l=1/2}$ , so the number of lines expected is ${displaystyle (2M_{1}l_{1}+1)(2M_{2}l_{2}+1)=[2(2)(1/2)+1][2(3)(1/2)+1]=12}$ which agrees with the observations.

RPE aspect of the metoxymethyl radical
The previous method can be extended to predict the number of lines for any number of cores.

While it is easy to predict the number of lines, the reverse action, interpreting a complex multi-line RPE spectrum and assigning the spaces to specific nuclei is more difficult.

In the common case of cores with spin ${displaystyle l=1/2}$ (e.g. ${displaystyle {ce {^1H, ^{19}F, ^{31}P}}}$ ), the intensity of the lines produced by a group of radicals, each with M equivalent nuclei will follow the triangle of Pascal. For example, the spectrum of the radical methyl shown above shows that the three cores of ${displaystyle {ce {^1H}}}$ of the radical give rise to four lines with a ratio 1:3:3:1 among them. The spacing between them corresponds to a constant of hyperfinal coupling ${displaystyle a_{H}=23 G}$ for each of the hydrogen cores. Note that the lines in the spectrum are the first ones derived from the absorptions.

As a second example, in the metoxymethyl radical ${displaystyle {ce {H3C(OCH2){.}}}}$ , center ${displaystyle {ce {OCH2}}}$ It will give a pattern of RPE 1:2:1, with each of its components subdivided by the three metoxi hydrogens in a pattern 1:3:3:1, giving a total of 12 lines, accommodated in a triplet of quartets. Note that the lesser coupling constants (lower space between lines) are due to the three metoxi hydrogens, while the larger coupling constants are due to the two hydrogens attached directly to the carbon atom shared by the broken electron. The common one that the constants of coupling diminish their value with the distance to an uneven electron, although there are notable exceptions such as the radical ethyl.

Definition of the width of the resonance signal

Resonance signal widths are defined in terms of magnetic induction B and its corresponding units are measured through the X axis of the rPE spectrums, from the center of the signal to a chosen reference point of the line. These defined widths are called midwidth and have some advantages: for asymmetric lines you can provide values of left and right middle widths. The average width ${displaystyle Delta B_{h}}$ is the measured distance from the center of the signal to the point where the absorption value equals half of the maximum absorption at the center of that resonance line. The first tilt width ${displaystyle Delta B_{1/2}}$ is the distance from the center of the signal to the maximum inclination point of the absorption curve. In practice, a complete definition of signal width is used. For symmetrical signals, average width ${displaystyle Delta B_{1/2}=2Delta B_{h}}$ and a full tilt width ${displaystyle Delta B_{max}=2Delta B_{1s}}$

Applications

This low-temperature ESR-STM device at the Center for Quantum Nanoscience is one of the first tunnel-effect microscopes to measure electronic spin resonance in individual atoms.

EPR/ESR spectroscopy is used in various branches of science such as biology, chemistry and physics for the detection and identification of free radicals in a solid, liquid or gaseous state, and in paramagnetic centers such as color centers. RPE spectroscopy is a sensitive and specific method for the study of both radicals formed during chemical reactions and for the study of the reactions themselves. An example of this is when water ice breaks down on exposure to high energy radiation and radicals such as H, OH and HO₂ are formed. Such radicals can be studied by RPE.

Organic and inorganic radicals can be detected in electrochemical systems and in materials exposed to UV light. In many cases, the reactions of formation of radicals and the subsequent reactions of such radicals are of interest, while in other cases the technique is used to provide information on the geometry of a radical or the orbital where the unpaired electron is found. EPR/ESR spectroscopy is also used in geology and archeology as a dating technique. It can be applied to a wide range of materials such as carbonates, sulfates, phosphates, silica, and silicates.

The RPE technique has proven to be a useful tool in research on homogeneous catalysis for the characterization of paramagnetic complexes and reactive intermediates. It is also particularly useful for investigating their electronic structures, fundamental to understanding their reactivity.

There are also medical and biological applications. Although radicals are highly reactive and therefore do not normally appear 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 non-reactive root molecules can attach to specific sites in a biological cell and the RPE spectrum can then provide information on the environment around these spin tags or root probes. Labeled fatty acids have been extensively used to study the dynamic organization of lipids in biological membranes, lipid-protein interactions, and transition temperatures of crystalline phases ranging from gels to liquids.

One type of dosimetry system has been designed for reference standards and routine use in medicine, based on radical RPE signals from irradiated polycrystalline α-alanine. This method is useful for measuring radiation doses from gamma rays, X-rays, electrons, protons, and high-energy linear transfers in the range of 1 Gy to 100 kGy.

EPR/ESR spectroscopy can only be applied to systems in which the balance between the decay of radicals and their formation maintains their concentration above the detection limit of the spectrometer used. This can be a particularly important problem in the study of reactions in liquids. An alternative approach is to study samples by heating reactions at cryogenic temperatures, such as 77 K (liquid nitrogen) or 4.2 K (liquid helium). An example of this is the study of 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) has the additional problem that tissues contain water and water, due to its electric dipole moment, has a high absorption band in the region of microwaves used by RPE spectrometers.

The technique has also been used by archaeologists in dating teeth. Radiation damage over long periods of time creates free radicals in tooth enamel, which can be examined and, after appropriate calibration, dated. Alternatively, material removed from people's teeth during dental procedures can be used to quantify their cumulative exposure to ionizing radiation. People who were exposed to radiation from the Chernobyl nuclear disaster have been examined using this method.

Foods that have been sterilized by radiation have been examined using this technique with the aim of developing methods to determine if the food has been irradiated and at what dose.

This type of spectroscopy has also been used to measure the microviscosity and micropolarity of drug transport systems as well as for the characterization of colloidal drug vehicles.

Measurements in high fields and high frequencies

RPE spectroscopy measurements at high fields and high frequencies are sometimes required to detect subtle details. However, for many years, the use of electromagnets producing fields above 1.5 T was impossible, mainly due to limitations of traditional magnetic materials. The first multifunctional millimeter RPE spectrometer with a superconducting solenoid was described in the early 1970s by the group of Professor Y.S. Lebedev (of the Russian Institute of Chemical Physics, in Moscow) in collaboration with the group of Professor L. G. Oranski (of the Ukranian Physics and Technics Institute, in Donetsk), who began to work at the institution of the former around 1975. Two decades later, a W-band RPE spectrometer was released as a small commercial line by The German Bruker Company, beginning the expansion of techniques of W-band RPE in medium-scale academic laboratories.


Banda	L	S	C	X	P	K	Q	U	V	E	W	F	D	-	J	-
${displaystyle lambda /mm}$	300	100	75	30	20	12.5	8.5	6	4.6	4	3.2	2.7	2.1	1.6	1.1	0.83
${displaystyle nu /GHz}$	1	3	4	10	15	24	35	50	65	75	95	111	140	190	285	360
${displaystyle B_{0}/T}$	0.03	0.11	0.14	0.33	0.54	0.86	1.25	1.8	2.3	2.7	3.5	3.9	4.9	6.8	10.2	12.8

The RPE band is dictated by the frequency or wavelengths of the spectrometer's microwave source as shown in the table above.

Variation of the RPE spectrum in the radical TEMPO (shown to the left) with the change of microwave band. Note how the resolution improves as the frequency increases.

RPE experiments are usually carried out in X bands and, less commonly, in Qs, mainly due to the availability of microwave components (originally developed for radars). A second reason for the widespread use of measurements in X and Q bands is that electromagnets can generate fields of about 1 tesla. However, the low spectral resolution due to factor g in these bands limits the study of paramagnetic centers with relatively low anisotropic magnetic parameters. Measurements to $nu$ 40 GHz in the millimetric region of wavelengths usually presents the following advantages:

The RPE spectrum is simplified due to the reduction of second order effects in high fields.
Increased selectivity of orientation and sensitivity in the research of disorderly systems.
The information and accuracy of pulse methods increases in high magnetic fields.
Accessibility of splint systems with greater zero field depopulation due to the increased quantum energy of microwaves.
Increased spectral resolution on factor g, which increases with radiation frequency ${displaystyle (nu)}$ and the outer magnetic field ${displaystyle B_{0}}$ . This is used to investigate the structure, polarity and dynamics of radical microcenters in organic and biological systems with spinal modifications through the markers. The figure shows how spectral resolution improves with increased frequency.
The saturation of paramagnetic centers occurs in microwave polarization fields ${displaystyle B_{1}}$ relatively low, due to the exponential dependence on the number of excited spins on the radiation frequency. This effect can be used to study the relaxation and dynamics of paramagnetic centers as well as superlent movements in the studied systems.
Cross relaxation of paramagnetic centers decreases in an important way in high magnetic fields, making it easier to obtain more accurate information and compet of the studied system.

This was demonstrated experimentally in the study of various biological systems, polymers, and other models in D-band spectroscopy.

Physical components of the equipment

Microwave Bridge

The microwave bridge contains both the microwave source and the detector. Older spectrometers used a vacuum tube called a klystron to generate microwaves, but modern spectrometers use a Gunn diode. Immediately after the microwave source is an isolator that serves to attenuate any reflection back to the source, which could result in microwave frequency fluctuations. The microwaves then pass through a directional coupler that splits the wave in two paths, one directed towards the cavity and the other directed to the reference arm. Across both paths is a variable attenuator that facilitates precise control of the microwave flow. This, in turn, allows control of the intensity of the microwaves delivered to the sample. On the reference arm, after the variable attenuator, is a phase shifter that establishes a defined phase relationship between the reference and the reflected signal, allowing sensitive phase detection.

Most RPE spectrometers are reflection spectrometers, which means that the detector should only be exposed to microwave radiation that is reflected from the cavity. This is accomplished through the use of a device known as a circulator, which directs microwave radiation into the cavity. The reflected microwave radiation, after absorption by the sample, passes through the circulator towards the detector, ensuring that it does not return to the microwave source. The reference signal and the reflected signal are combined and passed through the detector diode, which converts the microwave signal into an electrical current.

Reference arm

At low energies (less than 1 μW), the diode current is proportional to the microwave power and the detector is called a square law detector. At high 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. To obtain optimum sensitivity as well as quantitative information, the diode should operate within the linear region. To ensure that the detector is operating at that level, the reference arm serves to provide a reference.

Magnet

In an RPE spectrometer, the magnetic assembly includes a magnet with a dedicated power supply as well as a field detector or regulator such as a Hall effect sensor. RPE spectrometers use one of two types of magnets that is determined by the operating frequency of the microwaves (which also determines the range of magnetic field strength required). The first of these is an electromagnet that is generally capable of generating fields of up to 1.5 T, making it ideal for Q-band measurements. To generate fields suitable for W-band and higher, superconducting magnets are used. The magnetic field is homogeneous through the sample and has a high stability in static field.

Microwave Resonator (Cavity)

The microwave resonator is designed to improve the magnetic field of microwaves in the sample, with the objective of inducing RPE transitions. It is a metal box with rectangular or cylindrical shape that resonates with the microwaves (in the same way that an organ tube resonates with sound waves). At the frequency of cavity resonance, microwaves remain inside and are not reflected back. Resonance means that the cavity stores microwave energy and its ability to do so is given by the quality factor $Q$ defined by the equation:

${displaystyle Q={frac {2pi (energia almacenada)}{energia disipada}}}$

The higher the value of $Q$ , the higher the sensitivity of the spectrometer. Dissipated energy is the energy lost in a microwave period. The energy can be lost due to the side walls of the cavity, as the microwave generates currents that in turn generate heat. A consequence of resonance is the creation of static waves inside the cavity. The electromagnetic static waves have their electrical and magnetic field components exactly out of phase. This provides an advantage, as the electric field provides non-resonant microwave absorption, which increases energy dissipation and reduces the value of the microwave. $Q$ . To increase the signals and consequently increase the sensitivity, the sample is placed in a way that relapses into the maximum of the magnetic field and the minimum of the electric field. When the strength of the magnetic field is such that an absorption event occurs, the value of $Q$ will be reduced due to extra energy loss. This results in a change in impedance, which serves to stop the cavity of a critical coupling. This means that the microwaves will now be reflected back to the detector (on the microwave bridge) where an RPE signal will be detected.

Pulse Electron Paramagnetic Resonance

Electron spin dynamics is best studied with pulsed measurements. Microwave pulses, usually between 10 and 100 ns, are used to control the spins in the Bloch sphere. The relaxation time of the spin lattice can be measured with a payback experiment.

In a homologous way to the electronic magnetic resonance of pulse, Hahn's echo is central to most experiments. An echo decay experiment can be used to measure defasage time, as shown in animation. The size of the echo is recorded for different spaces of both pulses. This reveals decoherence, which is not recent by pulse $pi$ . In simple cases, an exponential decay is measured, which is described by time ${displaystyle T_{2}}$ .

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