Electron paramagnetic resonance (EPR) or electron spin resonance (ESR)
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
is a method for studying materials that have
unpaired electron
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 (specified by the three quantum numbers n, l and m) has a capacity to contain ...
s. The basic concepts of EPR are analogous to those of
nuclear magnetic resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
(NMR), but the
spins
The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of v ...
excited are those of the electrons instead of the
atomic nuclei
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
. EPR spectroscopy is particularly useful for studying metal complexes and organic radicals. EPR was first observed in
Kazan State University
Kazan (Volga region) Federal University (russian: Казанский (Приволжский) федеральный университет, tt-Cyrl, Казан (Идел буе) федераль университеты) is a public research uni ...
by
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
physicist
Yevgeny Zavoisky
Yevgeny Konstantinovich Zavoisky (russian: Евгений Константинович Завойский; September 28, 1907 – October 9, 1976) was a Soviet physicist known for discovery of electron paramagnetic resonance in 1944. He likely obse ...
in 1944, and was developed independently at the same time by
Brebis Bleaney
Brebis Bleaney (6 June 1915 – 4 November 2006) was a British physicist. His main area of research was the use of microwave techniques to study the magnetic properties of solids. He was head of the Clarendon Laboratory at the University of Ox ...
at the
University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
.
Theory
Origin of an EPR signal
Every electron has a
magnetic moment
In electromagnetism, the magnetic moment is 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 (such as electromagnets ...
and
spin quantum number
In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe th ...
, with magnetic components
or
. In the presence of an external magnetic field with strength
, the electron's magnetic moment aligns itself either antiparallel (
) or parallel (
) to the field, each alignment having a specific energy due to the
Zeeman effect
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
:
:
where
*
is the electron's so-called
''g''-factor (see also the
Landé ''g''-factor),
for the free electron,
*
is the
Bohr magneton
In atomic physics, the Bohr magneton (symbol ) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum.
The Bohr magneton, in SI units is defined as
\mu_\mathrm ...
.
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
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
's strength, as shown in the diagram below.
![EPR splitting](https://upload.wikimedia.org/wikipedia/commons/4/42/EPR_splitting.svg)
An unpaired electron can change its electron spin by either absorbing or emitting a
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
of energy
such that the resonance condition,
, is obeyed. This leads to the fundamental equation of EPR spectroscopy:
.
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
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
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.
![EPR Signal Harmonics](https://upload.wikimedia.org/wikipedia/commons/8/8b/EPR_Signal_Harmonics.svg)
For the microwave frequency of 9388.4 MHz, the predicted resonance occurs at a magnetic field of about
= 0.3350 T = 3350 G
Because of electron-nuclear mass differences, the
magnetic moment
In electromagnetism, the magnetic moment is 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 (such as electromagnets ...
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 above, 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
![EPR Field Modulation](https://upload.wikimedia.org/wikipedia/commons/e/ea/EPR_Field_Modulation.svg)
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.
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.
The same idea underlies the
Pound-Drever-Hall technique for frequency locking of lasers to a high-finesse optical cavity.
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
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
, and
is the
thermodynamic temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
. 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
In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
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:
* A high spectrometer frequency to minimize the Eq. 2. Common frequencies are discussed
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
*Bottom (disambiguation)
Bottom may refer to:
Anatomy and sex
* Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
* A low temperature to decrease the number of spin at the high level of energy as shown in Eq. 1. This condition explains why spectra are often recorded on sample at the
boiling point
The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.
The boiling point of a liquid varies depending upon the surrounding envir ...
of
liquid nitrogen
Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wide ...
or
liquid helium
Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.
At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temp ...
.
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:
# 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.
# Systems with multiple unpaired electrons experience electron–electron interactions that give rise to "fine" structure. This is realized as
zero field splitting
Zero field splitting (ZFS) describes various interactions of the energy levels of a molecule or ion resulting from the presence of more than one unpaired electron. In quantum mechanics, an energy level is called degenerate if it corresponds to two ...
and
exchange coupling, and can be large in magnitude.
# 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
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucl ...
, analogous to
''J''-coupling in NMR, splitting the EPR resonance signal into doublets, triplets and so forth. Additional smaller splittings from nearby nuclei is sometimes termed "superhyperfine" coupling.
# 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.
# These effects (''g''-factor, hyperfine coupling, zero field splitting, exchange 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
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
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.
![EPR g Matrix Rhombicity](https://upload.wikimedia.org/wikipedia/commons/f/fd/EPR_g_Matrix_Rhombicity.svg)
In general, the ''g'' factor is not a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
but a 3×3
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
. 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: ''g
xx'', ''g
yy'' and ''g
zz''. For a single spin experiencing only Zeeman interaction with an external magnetic field, the position of the EPR resonance is given by the expression ''g
xxB
x'' + ''g
yyB
y'' + ''g
zzB
z''. Here ''B
x'', ''B
y'' and ''B
z'' 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 (as in a fluid solution), the EPR spectrum consists of three peaks of characteristic shape at frequencies ''g
xxB''
0, ''g
yyB''
0 and ''g
zzB''
0.
In first-derivative spectrum, the low-frequency peak is positive, 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").
At higher temperatures, the three peaks coalesce to a singlet, corresponding to g
iso, for isotropic. The relationship between g
iso and the components is:
:
One elementary step in analyzing an EPR spectrum is to compare g
iso with the g-factor for the free electron, g
e. Metal-based radicals g
iso is typically well above g
e whereas organic radicals, g
iso ~ g
e.
The determination of the absolute value of the ''g'' factor is challenging due to the lack of a precise estimate of the local
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
at the sample location. Therefore, typically so-called ''g factor standards'' are measured together with the sample of interest. In the common spectrum, the spectral line of the ''g'' factor standard is then used as a reference point to determine the ''g'' factor of the sample. For the initial calibration of ''g'' factor standards, Herb et al. introduced a precise procedure by using double resonance techniques based on the
Overhauser shift.
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
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucl ...
constant of a nucleus is directly related to the spectral line spacing and, in the simplest cases, is essentially the spacing itself.
Two common mechanisms by which electrons and nuclei interact are the
Fermi contact interaction
The Fermi contact interaction is the magnetic interaction between an electron and an atomic nucleus. Its major manifestation is in electron paramagnetic resonance and nuclear magnetic resonance spectroscopies, where it is responsible for the appear ...
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.
In many cases, the isotropic hyperfine splitting pattern for a radical freely tumbling in a solution (isotropic system) can be predicted.
Multiplicity
![Methyl and Methoxymethyl Hyperfine Splitting](https://upload.wikimedia.org/wikipedia/commons/e/ef/Methyl_and_Methoxymethyl_Hyperfine_Splitting.svg)
* For a radical having ''M'' equivalent nuclei, each with a spin of ''I'', the number of EPR lines expected is 2''MI'' + 1. As an example, the methyl radical, CH
3, has three
1H nuclei, each with ''I'' = 1/2, and so the number of lines expected is 2''MI'' + 1 = 2(3)(1/2) + 1 = 4, which is as observed.
* For a radical having ''M''
1 equivalent nuclei, each with a spin of ''I''
1, and a group of ''M''
2 equivalent nuclei, each with a spin of ''I''
2, the number of lines expected is (2''M''
1''I''
1 + 1) (2''M''
2''I''
2 + 1). As an example, the methoxymethyl radical, 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 (2''M''
1''I''
1 + 1) (2''M''
2''I''
2 + 1) =
(2)(1/2) + 1 (3)(1/2) + 1= 3×4 = 12, again as observed.
* 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
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although ot ...
. For example, the spectrum at the right shows that the three
1H nuclei of the CH
3 radical give rise to 2''MI'' + 1 = 2(3)(1/2) + 1 = 4 lines with a 1:3:3:1 ratio. The line spacing gives a hyperfine coupling constant of ''a''
H = 23 ''G'' for each of the three
1H nuclei. Note again that the lines in this spectrum are ''first derivatives'' of absorptions.
As a second example, the methoxymethyl radical, H
3COCH
2. the OC''H''
2 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 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 (CH
2CH
3).
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
Absorption may refer to:
Chemistry and biology
* Absorption (biology), digestion
**Absorption (small intestine)
*Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials
*Absorption (skin), a route by which ...
value has half of maximal absorption value in the center of
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
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
![ESR-STM at QNS in Ewha - front view](https://upload.wikimedia.org/wikipedia/commons/6/66/ESR-STM_at_QNS_in_Ewha_-_front_view.jpg)
EPR/ESR spectroscopy is used in various branches of science, such as
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
,
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
and
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, for the detection and identification of
free radicals
In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron.
With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spont ...
in the solid, liquid, or gaseous state, and in paramagnetic centers such as
F-center
An F center or Farbe center (from the original German ''Farbzentrum'', where ''Farbe'' means ''color'' and ''zentrum'' means center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more un ...
s.
Chemical reactions
EPR is a sensitive, specific method for studying both radicals formed in chemical reactions and the reactions themselves. For example, when ice (solid H
2O) is decomposed by exposure to high-energy radiation, radicals such as H, OH, and HO
2 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 is useful in
homogeneous catalysis
In chemistry, homogeneous catalysis is catalysis by a soluble catalyst in a solution. Homogeneous catalysis refers to reactions where the catalyst is in the same phase as the reactants, principally in solution. In contrast, heterogeneous catalysis ...
research for characterization of
paramagnetic
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
complexes and
reactive intermediate
In chemistry, a reactive intermediate or an intermediate is a short-lived, high-energy, highly reactive molecule. When generated in a chemical reaction, it will quickly convert into a more stable molecule. Only in exceptional cases can these comp ...
s. EPR spectroscopy is a particularly useful tool to investigate their
electronic structure
In quantum chemistry, electronic structure is the state of motion of electrons in an electrostatic field created by stationary nuclei. The term encompasses both the wave functions of the electrons and the energies associated with them. Electro ...
s, which is fundamental to understand their
reactivity.
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
In physics, cryogenics is the production and behaviour of materials at very low temperatures.
The 13th IIR International Congress of Refrigeration (held in Washington DC in 1971) endorsed a universal definition of “cryogenics” and “cr ...
temperatures, such as 77 K (
liquid nitrogen
Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wide ...
) or 4.2 K (
liquid helium
Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.
At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temp ...
). 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.
Medical and biological
Medical
Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care practic ...
and
biological
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary in ...
applications of EPR also exist. Although radicals are very reactive, so they do not normally occur in high concentrations in biology, special reagents have been developed to attach "
spin label
A spin label (SL) is an organic molecule which possesses an unpaired electron, usually on a nitrogen atom, and the ability to bind to another molecule. Spin labels are normally used as tools for probing proteins or biological membrane-local dynami ...
s", also called "spin probes", to molecules of interest. Specially-designed nonreactive radical molecules can attach to specific sites in a
biological cell
The cell is the basic structural and functional unit of life forms. Every cell consists of a cytoplasm enclosed within a membrane, and contains many biomolecules such as proteins, DNA and RNA, as well as many small molecules of nutrients and ...
, and EPR spectra then give information on the environment of the spin labels. Spin-labeled fatty acids have been extensively used to study dynamic organisation of lipids in biological membranes, lipid-protein interactions and temperature of transition of gel to liquid crystalline phases. Injection of spin-labeled molecules allows for
electron resonance imaging Electron resonance imaging (ERI) is a preclinical imaging method, together with positron emission tomography (PET), computed tomography scan (CT scan), magnetic resonance imaging (MRI), and other techniques. ERI is dedicated to imaging small labora ...
of living organisms.
A type of
dosimetry Radiation dosimetry in the fields of health physics and radiation protection is the measurement, calculation and assessment of the ionizing radiation dose absorbed by an object, usually the human body. This applies both internally, due to ingested o ...
system has been designed for reference standards and routine use in medicine, based on EPR signals of radicals from irradiated polycrystalline α-
alanine
Alanine (symbol Ala or A), or α-alanine, is an α-amino acid that is used in the biosynthesis of proteins. It contains an amine group and a carboxylic acid group, both attached to the central carbon atom which also carries a methyl group side c ...
(the alanine deamination radical, the hydrogen abstraction radical, and the radical). This method is suitable for measuring
gamma
Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter re ...
and
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s, electrons, protons, and high-
linear energy transfer
In dosimetry, linear energy transfer (LET) is the amount of energy that an ionizing particle transfers to the material traversed per unit distance. It describes the action of radiation into matter.
It is identical to the retarding force acting on ...
(LET) radiation of
doses in the 1
Gy to 100 kGy range.
EPR can be used to measure
microviscosity
Microviscosity, also known as microscopic viscosity, is the friction experienced by a single particle undergoing diffusion because of its interaction with its environment at the micrometer length scale. The concept of microviscosity is intimately ...
and micropolarity within drug delivery systems as well as the characterization of colloidal drug carriers.
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
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
) has a strong absorption band in the
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
region used in EPR spectrometers.
Material characterization
EPR/ESR spectroscopy is used in geology and archaeology as a
dating tool. It can be applied to a wide range of materials such as organic shales, carbonates, sulfates, phosphates, silica or other silicates. When applied to shales, the EPR data correlates to the maturity of the kerogen in the shale.
EPR spectroscopy has been used to measure properties of
crude oil
Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crude ...
, such as determination of
asphaltene
Asphaltenes are molecular substances that are found in crude oil, along with resins, aromatic hydrocarbons, and saturates (i.e. saturated hydrocarbons such as alkanes). The word "asphaltene" was coined by Boussingault in 1837 when he noticed tha ...
and
vanadium
Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery-grey, malleable transition metal. The elemental metal is rarely found in nature, but once isolated artificially, the formation of an oxide layer ( pas ...
content. The free-radical component of the EPR signal is proportional to the amount of asphaltene in the oil regardless of any solvents, or precipitants that may be present in that oil. When the oil is subject to a precipitant such as
hexane
Hexane () is an organic compound, a straight-chain alkane with six carbon atoms and has the molecular formula C6H14.
It is a colorless liquid, odorless when pure, and with boiling points approximately . It is widely used as a cheap, relatively ...
,
heptane
Heptane or ''n''-heptane is the straight-chain alkane with the chemical formula H3C(CH2)5CH3 or C7H16. When used as a test fuel component in anti-knock test engines, a 100% heptane fuel is the zero point of the octane rating scale (the 100 point ...
,
pyridine
Pyridine is a basic heterocyclic organic compound with the chemical formula . It is structurally related to benzene, with one methine group replaced by a nitrogen atom. It is a highly flammable, weakly alkaline, water-miscible liquid with a d ...
however, then much of the asphaltene can be subsequently extracted from the oil by gravimetric techniques. The EPR measurement of that extract will then be function of the polarity of the precipitant that was used. Consequently, it is preferable to apply the EPR measurement directly to the crude. In the case that the measurement is made upstream of a
separator (oil production)
The term separator in oilfield terminology designates a pressure vessel used for separating well fluids produced from oil and gas wells into gaseous and liquid components. A separator for petroleum production is a large vessel designed to separate ...
, then it may also be necessary determine the oil fraction within the crude (e.g., if a certain crude contains 80% oil and 20% water, then the EPR signature will be 80% of the signature of downstream of the separator).
EPR 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. Similarly, material extracted from the teeth of people during dental procedures can be used to quantify their cumulative exposure to ionizing radiation. People (and other mammals) exposed to radiation from the atomic bombs, from the
Chernobyl disaster
The Chernobyl disaster was a nuclear accident that occurred on 26 April 1986 at the No. 4 reactor in the Chernobyl Nuclear Power Plant, near the city of Pripyat in the north of the Ukrainian SSR in the Soviet Union. It is one of only two nuc ...
, and from the
Fukushima accident
The was a nuclear accident in 2011 at the Fukushima Daiichi Nuclear Power Plant in Ōkuma, Fukushima, Japan. The proximate cause of the disaster was the 2011 Tōhoku earthquake and tsunami
The occurred at 14:46 JST (05:46 UTC) on 11 ...
have been examined by this method.
Radiation-sterilized foods have been examined with EPR spectroscopy, aiming to develop methods to determine whether a food sample has been irradiated and to what dose.
Other applications
In the field of
quantum computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
,
pulsed EPR
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 ...
is used to control the state of electron spin
qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
s in materials such as diamond, silicon and gallium arsenide.
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
The Institute of Problems of Chemical Physics (IPCP)See the web sitInstitute of Problems of Chemical Physics RAS (russian: Институт проблем химической физики РАН) of the Russian Academy of Sciences (RAS) is the la ...
,
Chernogolovka
Chernogolovka (russian: Черноголо́вка) is a town in Moscow Oblast, Russia. Center of the town is located some 43 km (27 miles) northeast of the Moscow city limit and 59 km (37 miles) from Red Square. Its population in 2018 ...
around 1975.
[EPR of low-dimensional systems]
/ref> Two decades later, a W-band EPR spectrometer was produced as a small commercial line by the German Bruker
Bruker Corporation is an American manufacturer of scientific instruments for molecular and materials research, as well as for industrial and applied analysis. It is headquartered in Billerica, Massachusetts, and is the publicly traded parent compa ...
Company, initiating the expansion of W-band EPR techniques into medium-sized academic laboratories.
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
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
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 are simplified due to the reduction of second-order effects at high fields.
# Increase in orientation selectivity and sensitivity in the investigation of disordered systems.
# The informativity and precision of pulse methods, e.g., ENDOR Endor or Ein Dor may refer to:
Places
* Endor (village), from the Hebrew Bible, a Canaanite village where the Witch of Endor lived
* Indur, a Palestinian village depopulated during the 1948 Arab-Israeli war
* Ein Dor, a Kibbutz in modern Israel
Fi ...
also increase at high magnetic fields.
# Accessibility of spin systems with larger zero-field splitting due to the larger microwave quantum energy ''h''.
# The higher spectral resolution over ''g''-factor, which increases with irradiation frequency and external magnetic field ''B''0. This is used to investigate the structure, polarity, and dynamics of radical microenvironments in spin-modified organic and biological systems through the spin label
A spin label (SL) is an organic molecule which possesses an unpaired electron, usually on a nitrogen atom, and the ability to bind to another molecule. Spin labels are normally used as tools for probing proteins or biological membrane-local dynami ...
and probe method. The figure shows how spectral resolution improves with increasing frequency.
# Saturation of paramagnetic centers occurs at a comparatively low microwave polarizing field ''B''1, 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.
# 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.
This was demonstrated experimentally in the study of various biological, polymeric and model systems at D-band EPR.
Hardware components
Microwave bridge
The microwave bridge contains both the microwave source and the detector. Older spectrometers used a vacuum tube called a klystron
A klystron is a specialized linear-beam vacuum tube, invented in 1937 by American electrical engineers Russell and Sigurd Varian,Pond, Norman H. "The Tube Guys". Russ Cochran, 2008 p.31-40 which is used as an amplifier for high radio frequenci ...
to generate microwaves, but modern spectrometers use a Gunn diode
A Gunn diode, also known as a transferred electron device (TED), is a form of diode, a two-terminal semiconductor electronic component, with negative resistance, used in high-frequency electronics. It is based on the "Gunn effect" discovered in 19 ...
. 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.[ 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 spectrometers 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
A circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an ...
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.
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
In electronic signal processing, a square law detector is a device that produces an output proportional to the square of some input.''IEEE Std. 100 Authoritative Dictionary of Standards Terms Seventh Edition'', IEEE, 2000, ,''Square law detection' ...
. 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".
Magnet
In an EPR spectrometer the magnetic assembly includes the magnet with a dedicated power supply as well as a field sensor or regulator such as a Hall probe
A Hall effect sensor (or simply Hall sensor) is a type of sensor which detects the presence and magnitude of a magnetic field using the Hall effect. The output voltage of a Hall sensor is directly proportional to the strength of the field. I ...
. EPR spectrometers 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.
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 , defined by the following equation:
The higher the value of 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 non-resonant absorption of the microwaves, which in turn increases the dissipated energy and reduces . 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 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.
Pulsed electron paramagnetic resonance
The dynamics of electron spins are best studied with pulsed measurements. Microwave pulses typically 10–100 ns long are used to control the spins in the Bloch sphere
In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix ...
. The spin–lattice relaxation time can be measured with an inversion recovery Inversion recovery is an MRI sequence that provides high contrast between tissue and lesion. It can be used to provide high T1 weighted image, high T2 weighted image, and to suppress the signals from fat, blood, or cerebrospinal fluid (CSF).
Fluid- ...
experiment.
As with pulsed NMR
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
, the Hahn echo In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.
The NMR ...
is central to many pulsed EPR experiments. A Hahn echo In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.
The NMR ...
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
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
is measured, which is described by the time.
Pulsed electron paramagnetic resonance could be advanced into electron nuclear double resonance Electron nuclear double resonance (ENDOR) is a magnetic resonance technique for elucidating the molecular and electronic structure of paramagnetic species.Kevan, L and Kispert, L. D. ''Electron Spin Double Resonance Spectroscopy'' Interscience: New ...
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
* Electric dipole spin resonance
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 ...
* Ferromagnetic resonance
Ferromagnetic resonance, or FMR, is coupling between an electromagnetic wave and the magnetization of a medium through which it passes. This coupling induces a significant loss of power of the wave. The power is absorbed by the precessing magneti ...
* Dynamic nuclear polarisation 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 ...
* Spin label
A spin label (SL) is an organic molecule which possesses an unpaired electron, usually on a nitrogen atom, and the ability to bind to another molecule. Spin labels are normally used as tools for probing proteins or biological membrane-local dynami ...
* Site-directed spin labeling Site-directed spin labeling (SDSL) is a technique for investigating the structure and local dynamics of proteins using electron spin resonance. The theory of SDSL is based on the specific reaction of spin labels with amino acids. A spin label's buil ...
* Spin trapping
* EDMR
Electrically detected magnetic resonance (EDMR) is a materials characterisation technique that improves upon electron spin resonance. It involves measuring the change in electrical resistance of a sample when exposed to certain microwave frequencie ...
* Optically detected magnetic resonance 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.
Like electron paramagnetic resonance (EPR), O ...
* Electron resonance imaging Electron resonance imaging (ERI) is a preclinical imaging method, together with positron emission tomography (PET), computed tomography scan (CT scan), magnetic resonance imaging (MRI), and other techniques. ERI is dedicated to imaging small labora ...
References
External links
Electron Magnetic Resonance Program
National High Magnetic Field Laboratory
Electron Paramagnetic Resonance (Specialist Periodical Reports)
Published by the Royal Society of Chemistry
The Royal Society of Chemistry (RSC) is a learned society (professional association) in the United Kingdom with the goal of "advancing the chemistry, chemical sciences". It was formed in 1980 from the amalgamation of the Chemical Society, the Ro ...
Using ESR to measure free radicals in used engine oil
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