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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electron paramagnetic resonance | 4/7 | https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance | reference | science, encyclopedia | 2026-05-05T10:04:27.171248+00:00 | kb-cron |
For a radical having M equivalent nuclei, each with a spin of I, the number of EPR lines expected is 2MI + 1. As an example, the methyl radical, CH3, has three 1H nuclei, each with I = 1/2, and so the number of lines expected is 2MI + 1 = 2(3)(1/2) + 1 = 4, which is as observed. For a radical having M1 equivalent nuclei, each with a spin of I1, and a group of M2 equivalent nuclei, each with a spin of I2, the number of lines expected is (2M1I1 + 1) (2M2I2 + 1). As an example, the methoxymethyl radical, H2C(OCH3) has two equivalent 1H nuclei, each with I = 1/2 and three equivalent 1H nuclei each with I = 1/2, and so the number of lines expected is (2M1I1 + 1) (2M2I2 + 1) = [2(2)(1/2) + 1] [2(3)(1/2) + 1] = 3×4 = 12, again as observed. The above can be extended to predict the number of lines for any number of nuclei. While it is easy to predict the number of lines, the reverse problem, unraveling a complex multi-line EPR spectrum and assigning the various spacings to specific nuclei, is more difficult. In the often encountered case of I = 1/2 nuclei (e.g., 1H, 19F, 31P), the line intensities produced by a population of radicals, each possessing M equivalent nuclei, will follow Pascal's triangle. For example, the spectrum at the right shows that the three 1H nuclei of the CH3 radical give rise to 2MI + 1 = 2(3)(1/2) + 1 = 4 lines with a 1:3:3:1 ratio. The line spacing gives a hyperfine coupling constant of aH = 23 G for each of the three 1H nuclei. Note again that the lines in this spectrum are first derivatives of absorptions. As a second example, the methoxymethyl radical, H3COCH2. the OCH2 center will give an overall 1:2:1 EPR pattern, each component of which is further split by the three methoxy hydrogens into a 1:3:3:1 pattern to give a total of 3×4 = 12 lines, a triplet of quartets. A simulation of the observed EPR spectrum is shown and agrees with the 12-line prediction and the expected line intensities. Note that the smaller coupling constant (smaller line spacing) is due to the three methoxy hydrogens, while the larger coupling constant (line spacing) is from the two hydrogens bonded directly to the carbon atom bearing the unpaired electron. It is often the case that coupling constants decrease in size with distance from a radical's unpaired electron, but there are some notable exceptions, such as the ethyl radical (CH2CH3).
=== Resonance linewidth definition === Resonance linewidths are defined in terms of the magnetic induction B and its corresponding units, and are measured along the x axis of an EPR spectrum, from a line's center to a chosen reference point of the line. These defined widths are called halfwidths and possess some advantages: for asymmetric lines, values of left and right halfwidth can be given. The halfwidth
Δ
B
h
{\displaystyle \Delta B_{h}}
is the distance measured from the line's center to the point in which absorption value has half of maximal absorption value in the center of resonance line. First inclination width
Δ
B
1
/
2
{\displaystyle \Delta B_{1/2}}
is a distance from center of the line to the point of maximal absorption curve inclination. In practice, a full definition of linewidth is used. For symmetric lines, halfwidth
Δ
B
1
/
2
=
2
Δ
B
h
{\displaystyle \Delta B_{1/2}=2\Delta B_{h}}
, and full inclination width
Δ
B
max
=
2
Δ
B
1
s
{\displaystyle \Delta B_{\text{max}}=2\Delta B_{1s}}
.
== Applications ==
EPR/ESR spectroscopy is used in various branches of science, such as biology, chemistry and physics, for the detection and identification of free radicals in the solid, liquid, or gaseous state, and in paramagnetic centers such as F-centers.
=== Chemical reactions === EPR is a sensitive, specific method for studying both radicals formed in chemical reactions and the reactions themselves. For example, when ice (solid H2O) is decomposed by exposure to high-energy radiation, radicals such as H, OH, and HO2 are produced. Such radicals can be identified and studied by EPR. Organic and inorganic radicals can be detected in electrochemical systems and in materials exposed to UV light. In many cases, the reactions to make the radicals and the subsequent reactions of the radicals are of interest, while in other cases EPR is used to provide information on a radical's geometry and the orbital of the unpaired electron. EPR is useful in homogeneous catalysis research for characterization of paramagnetic complexes and reactive intermediates. EPR spectroscopy is a particularly useful tool to investigate their electronic structures, which is fundamental to understand their reactivity. EPR/ESR spectroscopy can be applied only to systems in which the balance between radical decay and radical formation keeps the free radicals concentration above the detection limit of the spectrometer used. This can be a particularly severe problem in studying reactions in liquids. An alternative approach is to slow down reactions by studying samples held at cryogenic temperatures, such as 77 K (liquid nitrogen) or 4.2 K (liquid helium). An example of this work is the study of radical reactions in single crystals of amino acids exposed to x-rays, work that sometimes leads to activation energies and rate constants for radical reactions.