H. A. Farach and C. P. Poole, Jr., Department of Physics and Astronomy
University of South Carolina, Columbia, South Carolina 29208 USA

The phenomenon of electron spin resonance (ESR) is based on the fact that an electron is a charged particle which spins around its axis and this causes it to act like a tiny bar magnet. In technical language we say that it has a magnetic moment, the value of which is called the Bohr magneton.
If an external magnetic field Be is impressed on the system, the electron will align itself with the direction of this field and process around this axis. This behavior is analogous to that of a spinning top in the earth's gravitational field. Increasing the applied magnetic field will induce the electron to process faster and acquire more energy of motion called kinetic energy. In practice, the magnetic field will divide the electrons into two groups. In one group the magnetic moments of the electrons are aligned with the magnetic field, while in the other group the magnetic moments are aligned opposite or antiparallel to this external field.
Classically the needle of a compass points north, but if disturbed it could point in any direction. At the microscopic level of the electron, classical mechanics is replaced by quantum mechanics and one of the consequences is that the electron can only point either in the same direction as the external magnetic field or opposite to it. If perturbed only will point in one of the two directions but not in between. These two possible orientations in the applied field correspond to the projections Ms = 1/2 along the magnetic field direction where Ms is a dimensionless number used to designate the orientation. Each orientation is associated with a different energy, the one with the spins antiparallel to the external field (Ms = ­1/2) being the lower energy state.

If a second weaker alternating magnetic field B1 oscillating at a microwave frequency is now applied at right angles to the main field B0, then the electron can be "tipped" over when the microwave frequency is equal to the precession frequency. Another way to describe the phenomenon of ESR is to say that the quanta of the incident
microwaves induce transitions between the two states of the unpaired electron. When the energy hvof these quanta coincides with the energy level separation :

between the two states then resonance absorption of energy takes place.

The incoming radiation hv absorbed by the electrons in the lower energy level will induce these electrons to jump into the higher energy state. The incoming radiation is, however, also absorbed by the electrons in the higher energy level causing them to jump down to the lower level, a phenomenon called stimulated emission. Since the coefficients of absorption and stimulated emission are equal, no net value would be observed if the spin population were equally distributed between these two levels. In general, however, no, the population of the groundstate, exceeds n2, the population of the excited state, and a net absorption of microwave radiation takes place.

The population ratio of these two states at the temperature T can in most cases be described by the Boltzmann distribution

where k is a universal constant of nature called Boltzman's constant. A material containing atomic magnetic moments satisfying this Boltzmann distribution is called paramagnetic. Since E = hv at resonance the sensitivity of this technique is improved by using a high applied frequency. In practice, the most common frequencies in ESR are those in the well­developed radar wavebands. In addition, low operating temperatures are also beneficial for signal enhancement.

In most substances chemical bonding results in the pairing of the electrons which are transferred from one atom to another atom to form an ionic bond; or are shared between atoms to form a covalent bond so these materials are not magnetic. However, in a paramagnetic substance, i. e. one which contains unpaired electrons, resonance occurs at definite values of the applied magnetic field and incident microwave radiation.

At first glance one would expect the resonance spectrum of an unpaired electron to be always the same, but it is not because the magnetic behavior of the electron is modified by its surroundings. This modification of the resonance by the surroundings permits us to learn something about the structure of the material under study.
In a typical experiment the sample is placed in a resonant cavity which has a high quality factor or high Q. At a fixed microwave frequency o, and the magnetic field is varied until resonance occurs at the value Be given by
hv = gBo (2)

In this equation g is the "g­factor" which is a dimensionless constant and , is the unit magnetic moment of the spinning electron called the Bohr magneton .

In ESR it is customary to measure the g­factor. Some transition ions such as cobalt (Co2+) and copper (Cu2+) have g­values which differ significantly form g = 2, but free radicals have values that are fairly close to g = 2.0023 which characterizes a free electron.
Most ESR spectra are more complex than is implied by Equation 2. The resonant absorption is not infinitely narrow, which would be the case if absorption occurs at a precise value of the applied magnetic field. The actual line width ranges from a few milligauss for free radicals in solution to over 1000 gauss for some transition metal compounds in the solid state.
The reason for the finite line width B is that unpaired electrons not only interact with the externally applied magnetic field but also interact in a more or less random manner with the magnetic fields in their neighborhood. By observing this line width and line intensity, one can obtain information about the spin environment. Electron spin exchange between identical and non­identical molecules, chemical exchange between the paramagnetic molecule and its environment, and the interaction of nearby molecules having unpaired spins are some examples of environmental effects which can influence line width and intensity in the ESR spectrum.

An observed spectrum sometimes contains several lines referred to as hyperfine structure arising from the electrons interacting with nuclear spins denoted by I. The electronic spin of a transition metal ion usually interacts with its own nuclear spin, and in aromatic free radicals, the unpaired electron circulates among several atoms; and the resultant hyperfine structure is the result of the interaction of this electronic spin with several atoms such as hydrogen with nuclear spins. An example is the ethyl radical :

in which the unpaired electron ( ) interacts with the nuclear spins of two hydrogen atoms on the same carbon atom and also with the three hydrogens of the adjacent methyl group (CH3). The energy levels of an unpaired electron interacting with two nuclear spins is shown in Figure 1.

The simplest case is one in which there is no hyperfine interaction I=0). By placing the unpaired electron in a magnetic field, the number of energy levels is increased from one (E = Eo) to two (E = E0 1/2gH), as shown in the left portion of Figure 1.
The center and right side of the figure show cases where two nuclear spins with I=1/2 interact with the electron. A measure for the amount of interaction is given by the hyperfine coupling constant, Ai
Each nuclear spin I1 and I2 splits each original level into two levels. Hence, for A1 A2, the original two levels are split into 8 levels, as shown. Although there are 8 levels, only 4 transitions are possible because of the following selection rules.
MS = 1
MI = 0
where Ms is the electron spin quantum number and MI is the nuclear spin quantum number.

The hyperfine coupling constant Al with the nuclear species, and hyperfine splittings of the order of 10 millitesla or more can be observed. In organic compounds the electron may interact with several nuclei, and the hyperfine interactions may be as low as a few microtesla. The technique of ESR has been used to study many types of systems and we will comment on a few of them.
1. Biological Systems
ESR has been applied quite extensively to biological systems. One can follow the variations that occur under changing environmental conditions by monitoring the intensity of a free radical signal. For example, the presence of free radicals has been studied in healthy and diseased tissue. If a transition metal ion is present, as in case of the Fe ions of hemoglobin, then changes in its valence state may be studied by ESR. Early concrete evidence for the role of free radicals in photosynthesis, was provided by the observation of a sharp ESR resonance line. When incident light was turned off the resonance soon weakened or disappeared.
An inconvenience associated with the analysis of biological samples is the presence of water which produces high dielectric losses, making it necessary to use a flat quartz sample cell. Some typical systems which have been studied by ESR are hemoglobin, nucleic acids, enzymes, irradiated chloroplasts, riboflavin (before and after UV irradiation), and carcinogens.
2. Chemical Systems
A number of chemical substances such as synthetic polymers and rubber contain free radicals. The nature of the free radical depends upon the method of synthesis and on the history of the substance. Recent refinements in instrumentation have permitted the detection of free radical intermediates in chemical reactions.
Typical chemical systems that have been studied by ESR are polymers, catalysts, rubber, along­lived free radical intermediates, charred carbon, and chemical complexes with transition metals.
3. Conduction Electrons
Conduction electrons have been detected by both conventional electron spin resonance methods, and by the related cyclotron resonance technique. The latter employs and ESR spectrometer and the sample is located in a region of strong microwave electric field strength. In the usual ESR arrangement, on the other hand, the sample is placed at a position of strong microwave magnetic field strength. Conduction electrons have been detected in solutions of alkali metals in liquid ammonia, alkaline earth metals (fine powders), alloys (e. g., small amounts of paramagnetic metal alloyed with another metal), non­resonant absorption of microwaves by superconductors, and graphite.
4. Free Radicals
A free radical is a compound which contains and unpaired spin, such as the methyl radical CH3 produced through the breakup of methane
CH4CH3 + H (5)

where both the hydrogen atom and the methyl radical are electrically neutral. A charged free radical or radical ion is a neutral molecule which has gained or lost an electron

C6H6 + eC6H6 -(cation)
C6H6 e + C6H6+ (anion)

Free radicals have been observed in gaseous, liquid, and solid systems. They are sometimes stable, but can also be shod­lived intermediates in chemical reactions.
Free radicals and radical ions ordinarily have g­factors close to the free electron value of 2.0023 (e. g., for the stable free radical , ' diphenyl­-picryl­hydrazyl, referred to as DPPH, g = 2.0036). In low­viscosity solutions, radicals exhibit hyperfine patterns with a typical overall spread of about 2.5 millitesla. The scrupulous removal of oxygen often reveals hitherto unresolved structure. In a high­concentration solid a single exchange narrowed resonance appears (B~0.3 millitesla for DPPH prepared from benzene solution), whereas DPPH in a dilute oxygen free solution of the solvent tetrahydrofurane produces a spectrum with more than 100 hyperfine components.. In irradiated single crystals the free radicals may have strongly directionally dependent or anisotropic hyperfine interactions and slightly anisotropic g­factors.
Radical ions of many organic compounds can be produced in an electrolytic cell which is usually a flat quartz cell with a mercury pool cathode and a platinum anode. This electrolytic cell may be mounted in a flat measuring cell located in the resonance cavity. When the applied voltage in the electrolytic system is increased, the current will first increase, but soon levels off to a plateau. Radical ions are formed in this plateau region. Radical formation can sometimes be observed visually because of color changes in the solution. Since oxygen is also paramagnetic, dissolved air must be scrupulously removed prior to the experiment. The best method is to use the freeze­pump­thaw technique where the sample is first frozen and then connected to a high vacuum source. After closing off the vacuum pump, the sample is melted and refrozen. Several cycles are sufficient to remove the oxygen.
5. Irradiated Substances
A considerable amount of work has been done on radiation induced free radicals in organic compounds and paramagnetic color centers in ionic solids. Most irradiations are carried out with x­rays, gamma­rays, or electrons whose energies far exceed chemical bond energies, although paramagnetic spins can also be produced by less energetic ultraviolet light or neutrons. Most of these spectra are obtained after the sample is irradiated, and many paramagnetic centers are found to be sufficiently long­lived to warrant such a
procedure. More sophisticated experimental techniques entail simultaneous irradiation and ESR detection. Low­temperature irradiation and detection can reveal the presence of new centers which can be studied at gradually increasing temperatures to elucidate the kinetics of their recombination.
6. Naturally Occurring Substances
Most of the systems studied by ESR are synthetic or man­made. Nevertheless, from the beginning of the field, various naturally occurring substances have been studied, such as: (1) minerals with transition elements [e. g., ruby (Cr/Al2O3), dolomite Mn/(Ca, Mg(Co3)]; (2) minerals with defects (e. g., quartz); (3) hemoglobin (Fe); (4) petroleum; (5) coal; (6) rubber; and (7) various biological systems.
7. Spin labels
There are a number of free radicals called spin labels which can attach themselves to particular sites in biological systems and produce spectra which provide information on changes in the chemical and physical characteristics in the neighborhood of the site. An example of a spin label has its unpaired electron on the NO group of a nitroxyl compound such as 2, 2, 6, 6­tetramethyl-4­piperadone­1­oxyl

The unpaired electron shown on the lower oxygen, spends time on and strongly interacts with the I = 1 nuclear spin of the nitrogen atom to produce a 3­line hyperfine spectrum. When the solvent has a low viscosity (flows very freely) the radical tumbles rapidly to average out the anisotropies, and a spectrum of three narrow lines is obtained. At lower temperatures the viscosity increases and the solvent materials flows very slowly so the nitrogen radical can no longer tumble rapidly, and a smeared out spectrum is produced.
When the spin label attaches itself to a particular site in a biological molecule its spectrum reveals the extent to which free motion or very restricted motion occurs at the site. Different spin labels have been synthesized which attach themselves to very specific sites. For example the spin label n­doxylstearic has the nitroxide doxyl group attached to different positions n between 5 and 16 on the long stearic acid molecule. This spin label can be inserted into a cell membrane so each value of n corresponds to a different depth in the membrane, and a sequence of labels provides information on the activities of the membrane at various depths below the surface.
Two chapters in Ref. 1 recount the history of ESR, Chap. 1 of Ref. 2 serves as an entree to the extensive literature, and Chap. 1 of Ref. 3 provides a more extensive introduction to the subject. The theoretical underpinning is surveyed in Refs. 4 and 5.

1. G. R. Eaton and S. S. Eaton, EPR at 50, in press. See Chapters "Preparing the way for Paramagnetic Resonance" and "The First Sesquidecade of Paramagnetic Resonance" by C. P. Poole, Jr. and H. A. Farach.

2. C. P. Poole, Jr. and H. A. Farach, Handbook of Electron Spin Resonance, American Institute of Physics Press, NY, 1994, see Chap. 2. Data Sources.

3. F. J. Owens, C. P. Poole, Jr., and H. A. Farach, Magnetic Resonance of Phase Transitions, Academic Press NY 1979; see Chap. 1 Magnetic Resonance as a Probe of Phase Transitions.

4. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Dover NY 1986.

5. C. P. Poole, Jr. and H. A. Farach Theory of Magnetic Resonance 2nd Edition Wiley NY 1987.