Electron Spin Resonance (ESR)

Principle

Electron Spin Resonance (ESR) or Electron Paramagnetic Resonance (EPR) is a spectroscopic technique (see Spectroscopy) which detects atoms that have unpaired electrons. It means that the molecule in question is a free radical if it is an organic molecule. Because most stable molecules have a closed-shell configuration of electrons without a suitable unpaired spin, the technique is less widely used than nuclear magnetic resonance, NMR. (Spin refers to rotating of an object around some axis trough the object.)

The basic physical concepts of the technique are analogous to those of NMR, but instead of the spins of the atom's nuclei, electron spins are excited. Because of the difference in mass between nuclei and electrons, some 10 times weaker magnetic fields and higher frequencies are used, compared to NMR. For electrons in a magnetic flux field (or magnetic induction) of 0.3 T (tesla), spin resonance occurs at around 10 GHz. (1 T = 1 N/(Am) = 10.000 Gauss = 10⁹ gammas).

Application

ESR is used in solid-state physics for the identification and quantification of radicals (i.e., molecules with unpaired electrons), in (bio)chemistry to identify reaction pathways. Its use in biology and medicine is more complicated. This group can be used to couple the probe to another molecule, e.g. a bio-molecule).

Since radicals are very reactive, they do not normally occur in high concentrations in biological environments. With the help of specially designed non-reactive, so stable free radical molecules carrying a functional group that attach to specific sites in a biological cell, it is possible to quantify structures comprising these sites with these so-called spin-label or spin-probe molecules.

To detect some subtle details of some systems, high-field-high-frequency electron spin resonance spectroscopy is required. While ESR is affordable for a medium-sized academic laboratory, there are few scientific centers in the world offering high-field-high-frequency electron spin resonance spectroscopy.

More Info

An electron has a magnetic moment (≡ torque/magnetic field strength, in Am²) and spin quantum number s = 1/2, with magnetic components m_s = +1/2 and m_s = -1/2. When placed in an external magnetic field of strength B₀, this magnetic moment can align itself either parallel (m_s = -1/2) or antiparallel (m_s = +1/2) to the external field. The former is a lower energy state than the latter (this is the Zeeman effect), and the energy separation between the two is:

ΔE = g_eμ_BB₀, (1)

where g_e is the gyromagnetic ratio or g-factor of the electron, a dimensionless quantity. It is the ratio of its magnetic dipole moment to its angular momentum. The magnetic moment in a magnetic field is a measure of the magnetic flux set up by the rotation (spin and orbital rotation) of an electric charge in a magnetic field. Further, μ_B is the Bohr magneton (a constant of magnetic moment μ_B = 9.27 x 10^-24 Am²) and B₀ the magnetic field strength (N/A∙m).

An unpaired electron can move between the two energy levels by either absorbing or emitting electromagnetic radiation of energy ε = hν (Planck’s constant times frequency) such that the resonance condition, ε = ΔE, is obeyed. Substituting in ΔE = hν in (1) gives:

hν = g_eμ_BB₀. (2)

This is the fundamental equation of EPR spectroscopy.

This equation implies that the splitting of the energy levels is directly proportional to the magnetic field's strength, as shown in Fig. 1.

Fig. 1

A collection of paramagnetic molecules (molecules with the property to align in a magnetic field, see Diamagnetism and paramagnetism), such as free radicals, is exposed to microwaves at a fixed frequency. By increasing an external magnetic field, the gap between the m_s = +1/2 and m_s = -1/2 energy states is widened until it matches the energy of the microwaves, as represented by the double-arrow in Fig. 1. At this point the unpaired electrons can move between their two spin states. Since there typically are more electrons in the lower state, there is a net absorption of energy, and it is this absorption which is monitored and converted into a spectrum.

A free electron (on its own) has a g value of about 2.0023 (which is g_e, the electronic g factor). This means that for radiation at the commonly used frequency of 9.75 GHz (known as X-band microwave radiation, and thus giving rise to X-band spectra), resonance occurs at a magnetic field of about 0.34 tesla.

ESR signals can be generated by resonant energy absorption measurements made at different electromagnetic radiation frequencies ν in a constant external magnetic field (i.e. scanning with a range of different frequency radiation whilst holding the field constant, like in an NMR experiment). Conversely, measurements can be provided by changing the magnetic field B and using a constant frequency radiation; due to technical considerations, this second way is more common. This means that an ESR spectrum is normally plotted with the magnetic field along the horizontal axis, with peaks at the field that cause resonance (whereas an NMR spectrum has peaks at the frequencies that cause resonance).

For more information see e.g. the Wikipedia chapter on ESR.