Introduction

Electron Paramagnetic Resonance (EPR), also known as Electron Spin Resonance (ESR), is a versatile, non-destructive spectroscopical technique used to investigate chemical species with unpaired electrons. These include organic free radicals, defects in solids and compounds of transition metal ions with unpaired electrons.^[1] EPR was discovered by the Russian scientist Zavosky in 1945 and since then it has become one the most powerful techniques for the analysis of condensed matter. ^[2] Electron spin resonance is used in different fields such as physics, chemistry, biology, life science, material science, medicine, and food science.^[1]

Basic Principles of EPR

Fundamental concepts

Similarly to Nuclear Magnetic Resonance (NMR), EPR involves the interaction of electromagnetic radiations, usually microwaves, with frequencies between 9000-10000 MHz, with the paramagnetic material, in presence of an external magnetic field.^[3]Every electron is characterized by an intrinsic spin quantum number s =1/2, with magnetic components m_s=±1/2.^[4] Because of its spin, an electron behaves like a small magnet. ^[3] When we introduce the electron in an external magnetic field, the electron’s magnetic moment aligns either parallel (m_s=1/2) or antiparallel (m_s=-1/2) to the magnetic field. These two configurations have different energies. Electrons aligned parallel to the external magnetic field occupy a lower energy level compared to the antiparallel configuration. This creates a difference in energy (ΔE) that can be calculated as

ΔE=gBμ

where g is the spectroscopic splitting factor, which for an electron in vacuum has the value of 2.002319, μ is the Bohr magneton and B is the external magnetic field. The values so obtained are called Zeeman energies. When the system is hit with electromagnetic radiation, if the energy of the incident photon corresponds to the energy gap, the system can adsorb the photon. This causes the excitation of the electron which flips its spin, assuming the higher energy configuration. 

ΔE=hν=gBμ

After a particular relaxation time the system goes back to its more stable configuration, releasing a photon which has the same energy of the gap ΔE. The spin configurations are illustrated in Figure 1.^[5]

Figure 1. Spin configurations in a magnetic field. Figure: Elisa Crocioni.

Detecting the energy released by these electrons, a spectrum is obtained. The observation of one or more lines in the record indicates the presence of unpaired spins and the intensity indicates their number. Like other spectroscopical techniques, EPR analyzes the absorption of electromagnetic radiation. The phase sensitive detector, although, transforms the normal absorption signal into its first derivative and this explains why the spectrum is characterized by symmetric maximums and minimums around the center of the signal.^[6] From the spectrum we can identify the nature of the paramagnetic centre, the nature of the complex (next neighbor and symmetry), distribution of unpaired spin density and number of paramagnetic centers. ^[7]

Hyperfine splitting

The spectrum obtained with EPR may consist of a single line or multiple lines and it might change due to the temperature and the orientation of the sample.^[6]  Since the source of the EPR spectrum is the change of an electron spin state, if we have a system of one electron, the spectrum only consists of one line. However, the electron spin couples with the nuclear spin due to the fact that the electrons experience the magnetic field of the nucleus of the molecule. This is called hyperfine interaction. The coupling introduces new energy states and consequently a multiline spectra. Since a nucleus with a spin of I has (2I+1) spin states, the EPR spectrum will have (2I+1) lines. Since the number of lines depends on the nuclear spin l, hyperfine interaction is useful to identify the presence of radicals.^[2]  The magnitude of the hyperfine splitting is defined by a coupling constant which is measured in MHz. The larger the number of nuclei in the system, the further the split for every nuclear interaction.^[1]

Fine structure interactions 

The magnetic moment of electron is larger in comparison to the magnetic moment of protons and neutrons, so the interactions between electrons have higher energies than the ones with nuclear spin and can be detected over higher distances. The electron-electron spin interactions can cause splitting or broadening of the EPR signal. For solid paramagnetic materials the broadening may be so great that the EPR spectrum becomes undetectable.^[1]

Experimental procedure

EPR spectrometer

Since its development, the design of the EPR spectrometer has remained almost unchanged but its use has been increasing in different fields of physics, chemistry and biochemistry.^[1]

A conventional continuous wave spectrometer is composed of four parts: source components, magnet system, detection system and modulation system (Figure 2). The source creates a monochromatic beam of a specific frequency and directs it toward the sample that we want to analyze which is located into a resonant cavity. The sample is usually collocated in a point of the cavity where the microwave magnetic field is greatest.^[5]  The microwave source is usually a reflex klystron (a type of thermionic valve) or a Gunn diode (a semiconductor device). 

The bandwidth in EPR is greater than the one of NMR and it is impossible to adjust the frequency of the radiation in such a big range. For this reason the spectra is usually obtained keeping the frequency constant and changing the value of the external magnetic field.^[1]

The magnet creates the magnetic field which is necessary to allow the spin splitting fenomena and to obtain the spectrum. The detection and modulation system (usually a wave diode) receive and record the signal.^[5]

The sample can be liquid, solid or gas and for this reason a proper temperature control is needed. This can be done flowing gas (He or N₂) in the system. Differently from NMR, the relaxation rate of the spin is faster for electrons, this can require the system to be brought to cryogenic temperatures to be able to see the spectrum.^[1]

Figure 2. EPR spectrometer. Figure: Elisa Crocioni.

Sample preparation

For solution EPR samples, a low dielectric solvent has to be chosen in order not to lower the sensitivity of the resonator and to get a valid spectrum. Samples must be frozen in liquid nitrogen before being introduced into the cryostat.

Solid samples are analyzed as powders. They are positioned into tubes and the tubes are flushed with gaseous helium to avoid the formation of air ice around the sample. The latter, in fact, can cause the sample to become an insulator, causing the temperature inside the sample to be higher than the external temperature of the system.^[8]

Pulsed EPR

A variation of EPR is pulsed EPR. The layout of the spectrometer is the same of classic EPR but in addition a pulse programmer controls the microwave supply using diode switches. The pulses have duration that varies from 5 to 50 ns and they are amplified using traveling-wave tube amplifiers.^[7] 

Examples

Many rare isotopes of metals were analyzed using EPR in early days. Today, because of the simplicity of reaching lower temperatures and the fact that most nuclear spins are known, the interest moved to the identification of radicals produced by radiation damage.^[1] EPR spectra for methyl and methoxymethyl radicals can be seen in the Figure 3.

Figure 3. EPR spectra for methyl and methoxymethyl radicals. Figure from Wikipedia. (License: CC0 1.0)

Comparison of EPR and NMR

Both EPR and NMR are absorption spectroscopical techniques that analyze the spin state splitting due to the introduction of the sample in an external magnetic field. The main difference between the two is that while EPR describes the magnetically induced splitting of electronic spin states, NMR shows the splitting of nuclear states. In EPR it is necessary for the electrons to be in a state of non-zero total angular momentum, which means that if we consider atoms with a close shell configuration, no spectrum will be obtained. In order to obtain a spectrum in NMR, instead, the total electronic spin must be zero.

The bandwidth in EPR is larger than the one of NMR and it is impossible to adjust the frequency of the radiation in such a big range. For this reason in EPR the frequency is kept constant while the value of the magnetic field changes, while in NMR the value of the magnetic field is kept constant.

Another main difference is associated to the experimental process. EPR usually requires radiation of microwave frequency (GHz), while in NMR lower frequencies are necessary, usually MHz.^[9]

Bibliography