Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes and 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.

Theory

Origin of an EPR signal

Every electron has a magnetic moment and spin quantum number ${\displaystyle s={\tfrac {1}{2}}}$, with magnetic components ${\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}}$ or ${\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}}$. In the presence of an external magnetic field with strength ${\displaystyle B_{\mathrm {0} }}$, the electron's magnetic moment aligns itself either antiparallel (${\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}}$) or parallel (${\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}}$) to the field, each alignment having a specific energy due to the Zeeman effect:

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

where

• ${\displaystyle g_{e}}$ is the electron's so-called g-factor (see also the Landé g-factor), ${\displaystyle g_{\mathrm {e} }=2.0023}$ for the free electron,^[3]
• ${\displaystyle \mu _{\text{B}}}$ is the Bohr magneton.

Therefore, the separation between the lower and the upper state is ${\displaystyle \Delta E=g_{e}\mu _{\text{B}}B_{0}}$ for unpaired free electrons. This equation implies (since both ${\displaystyle g_{e}}$and ${\displaystyle \mu _{\text{B}}}$ are constant) that the splitting of the energy levels is directly proportional to the magnetic field's strength, as shown in the diagram below.

An unpaired electron can change its electron spin by either absorbing or emitting a photon of energy ${\displaystyle h\nu }$ such that the resonance condition, ${\displaystyle h\nu =\Delta E}$, is obeyed. This leads to the fundamental equation of EPR spectroscopy: ${\displaystyle h\nu =g_{e}\mu _{\text{B}}B_{0}}$.

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 ${\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}}$ and ${\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}}$ 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.

For the microwave frequency of 9388.4 MHz, the predicted resonance occurs at a magnetic field of about ${\displaystyle B_{0}=h\nu /g_{e}\mu _{\text{B}}}$ = 0.3350 T = 3350 G

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 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 ${\displaystyle h\nu =g_{\mathrm {N} }\mu _{\mathrm {N} }B_{0}}$ where ${\displaystyle g_{\mathrm {N} }}$ and ${\displaystyle \mu _{\mathrm {N} }}$ depend on the nucleus under study.)

Field modulation

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.

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 Boltzmann distribution:

${\displaystyle \frac{n_{\text{upper}}}{n_{\text{lower}}}=\exp <!--\; \; -->(-<!--\; -\; -->\frac{E_{\text{upper}}}{}}$Zdroj:https://en.wikipedia.org?pojem=Electron_paramagnetic_resonance
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