What is EPR?

Electron Paramagnetic Resonance (EPR) alias Electron Spin Resonance (ESR) is a physical phenomenon of absorption of electromagnetic radiation by a special type of molecules placed in a magnetic field.

These special molecules are called paramagnetic because they have a not equal to zero total electron spin and therefore can be considered as small magnets. A typical example of paramagnetic molecules is free radicals - chemically active and therefore usually short lived species.

In a sample containing paramagnetic species, all non-zero spins (the tiny magnets) are oriented chaotically and have the same energy, as shown in the figure on the left.

We are now going to apply an external magnetic field to such a sample. What happens next is most important for understanding the phenomenon of EPR.

Once an external magnetic field of a magnitude, say, H1 is switched on (figure below), all the paramagnetic species, oriented chaotically before, are now re-oriented in two possible ways. Most of the magnets will align their magnetic axes along the direction of the external magnetic field. There will be also a fraction of magnets (smaller in number) aligned against that direction. The latter population, being less favourable, would have a higher energy. Therefore, these two groups of the paramagnetic specis will have different energy, and it is said that the energy of paramagnetic species splits in the external magnetic field, the greater the field, the greater the distance between the two energy levels.
There are two coefficients of proportionality in this linear dependence (as shown in the figure above). One is called the Bohr magneton b, which is a combination of fundamental constants and therefore is the same for all paramagnetic species. The other one is called the g-factor. It is paramagnetic species specific and can vary significantly for paramagnetic species of different nature. For example, the g-factor of free radicals is close to the value of 2, whereas the g-factor of paramagnetic metals, for example of iron in haemoglobin, can be as high as 6.

Thus, the energy split in the figure above, when an external magnetic field H1 is applied, is DE = gbH1.

The figure below shows what happens when we start increasing the external magnetic field while continuously irradiating the sample with an electromagnetic radiation. The frequency of the radiation n is kept constant (in the microware radiation range), which makes the energy of the radiation quanta hn constant, too.
The distance between these two levels will start to increase. Now the magnetic field is repeatedly scanned form the value H1 to a value H2. The distance between the energy levels DE is increasing with the field. At some point, at a magneti field of Ho, this distance becomes equal to the energy of microwave radiation hn. And it is at this point that the transitions between the levels occur, or we can say that the electron spins flip. This is the resonance, the electron paramagnetic resonance. It occurs when the energy of microwave radiation equals to the distance between the levels with opposite spin orientations. This condition is described by the resonance formula:

hn = gbHo

The spin transition between the levels requires energy which is taken from the microwave radiation. The microwave energy absorption can be measured quantitatively, this is exactly what an EPR spectrometer does.

The method of EPR spectroscopy has numerous applications in chemistry, biology, medicine.
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