Abstract
Magnetic resonance is divided into electron spin resonance (ESR) [electron paramagnetic resonance (EPR)] and nuclear magnetic resonance (NMR) according to the working region in the electromagnetic spectrum. If the studied region is in the microwave region, this resonance type is electron spin resonance. If the region studied is the radio frequency region, then nuclear magnetic resonance is mentioned. ESR and NMR are similar in terms of their basic theorem.
Keywords
- electron spin resonance (ESR)
- electron paramagnetic resonance (EPR)
- nuclear magnetic resonance (NMR)
- microwave frequency
- radio frequency
1. Introduction
Nuclear magnetic resonance (NMR) spectroscopy examines the interaction of nuclear spins forming an atom with the magnetic field applied to them. Electron spin (paramagnetic) resonance (ESR, EPR) spectroscopy studies the interaction of the electron spins with the applied magnetic field.
The resonance term is used to determine that an external factor is in harmony with the natural frequency of the magnetic system. The natural frequency is the radio frequency (RF) or microwave (MD) frequency, which is in agreement with the Larmor rotation frequency of the magnetic moments in the magnetic field.
The magnetic moment referred to NMR is a nonzero nuclear moment. In other words, NMR deals with nuclei whose spin value is nonzero. The magnetic moment referred to EPR is the magnetic moment of the electron. EPR studies magnetic systems with unpaired electrons.
2. Magnetic resonance spectroscopy (NMR and EPR spectroscopy)
Nuclear magnetic resonance (NMR) was first observed by F. Bloch in 1946. In the same period, the electron spin resonance (ESR) experiment was first performed by YK Zavoysky in 1944.
Magnetic resonance spectroscopy is similar to other types of absorption spectroscopy. Magnetic resonance is based on the interaction of matter with electromagnetic radiation. Electromagnetic radiation for NMR is in the radio frequency domain. For the EPR, it is in the microwave area. As a result of this interaction, the transition from the high energy state to the low energy state leads to an energy release in the amount of (∆
Within the external magnetic field, the magnetic moment of the nucleus or electron makes a precession movement with the Larmor frequency (
The state of the system reaching the thermal equilibrium is called relaxation time. Relaxation times are divided into two. The first is
The orientations of the magnetic moments are in the form of different spin populations at different energy levels. Boltzmann expression is used for low energy state (
where
The ratio of the magnetic moment to the spin angular momentum is
where
This expression contains both the resonance condition and the magneton concept. For EPR studies, Bohr magneton is valid whereas for NMR studies nuclear magneton is applied. Magneton is related to the concept of spin magnetic moment (
where
where
or
Since
The above expression is called resonance condition in both NMR and ESR [1].
Although many processes are similar in the EPR and NMR experiments, the tools used in the experiments differ. In EPR, it is used in microwave components, such as wave-guide, cavities, and klystron tubes. In NMR, inductances, capacitors, conductors that transmit radio frequency energy, and vacuum tubes are used [2].
2.1. NMR spectroscopy
Magnetic dipole moment of the nucleus:
Here,
The interaction between the external magnetic field and the nuclear magnetic moment is given as follows:
where
The nuclear magnetic resonance transition occurs between two energy levels. The transition between the two energy levels constitutes the resonance condition.
is called
Nuclear magnetic resonance stays on two important interactions. The first one is
The chemical shift
The spin-spin coupling
The exchange interaction
Slow exchange interaction
Fast exchange interaction
However, the third influence is not taken into consideration. So, we will focus on two interactions.
Here,
2.1.1. Chemical shift
The electrons surrounding the nucleus of a molecular system show a spherical distribution. The external magnetic field applied on the system creates polarity in the electron distribution in the spherical structure. That is, a current flows through the molecule. This current induces a magnetic field by induction where the core is located. This field is called
Accordingly, the nucleus sees the effective magnetic field given by the formula:
The internal magnetic field is connected to the external magnetic field (Eq. (18))
The internal magnetic field is connected to the external magnetic field by
2.1.2. Spin-spin coupling
Contrary to the dipole-dipole interaction, it is a new type of interaction that is not dependent on the orientation of the molecule. It is the indirect spin-spin interaction period that occurs through the electrons that form chemical bonds in the molecule. In other words, the interaction of a nucleus with another nucleus through an electron cloud is a spin-spin coupling. The spin of an electron near the
When a nucleus or nucleus group interacts with
2.2. EPR (ESR) spectroscopy
EPR is a magnetic resonance method such as NMR. EPR deals with substance that contains unpaired electrons. These substances are free radicals, triplet excited states, and most transition metal and rare earth species. Among the parameters found in the EPR experiments are the g-factor, the hyperfine structure constant (
For EPR analysis, the sample is placed in a strong magnetic field. The applied electromagnetic radiation is in the microwave area. Due to the interaction between the magnetic moment of the free electron and the external magnetic field, the spin of the electron is directed parallel or antiparallel to the magnetic field. The energy difference between the two orientations gives the resonance condition for EPR.
Here,
Magnetic dipole moment of the free electron:
where
The interaction between the external magnetic field and the magnetic moment of the free electron is given as follows:
where
The electron spin resonance transition occurs between two energy levels. The transition between the two energy levels constitutes the resonance condition.
is called
2.2.1. g-factor
The unpaired electrons can cause a slight shift in the resonance line due to the internal magnetic field effect. This effect is expressed as a
To calculate the
The
2.2.2. Hyperfine coupling
The interaction between the unpaired electron and the nucleus is called the hyperfine structure interaction. For hyperfine structure interaction, the nuclear spin value must be different from zero (
where |
For the anisotropic hyperfine structure interaction, it is expressed as:
where
In the same way, the average of the diagonal elements of the
An example of an EPR spectrum is shown in Figure 7.
The difference between the hyperfine structure splitting of two inequivalent protons and the hyperfine structure splitting of two equivalent protons is shown in Figures 9 and 10, respectively.
The hyperfine structure interaction in the EPR is identical to the spin-spin coupling interaction in NMR.
3. Conclusion
EPR and NMR form the magnetic resonance spectroscopy. EPR and NMR depend on the same basic principles. However, these two experimental methods differ because of the differences in the physical quantities between the electron and the nucleus. These differences stand out in terms of charge, mass, and magnetons (Bohr magneton or nuclear magneton).
References
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Varian Associates. Instrument Division. NMR and EPR Spectroscopy. Papers presented at Varian’s Third Annual Workshop on Nuclear Magnetic Resonance and Electron Paramagnetic Resonance, held at Palo Alto, California. Oxford: Pergamon Press; 1960. pp. 1-3 - 3.
Poole CP, Jr., Farach HA. The Theory of Magnetic Resonance. New York: Wiley-Interscience; 1972. pp. 1-270 - 4.
Weil JA, Bolton JR, Wertz JE. Electron Paramagnetic Resonance: Elementary Theory and Practical Applications. New York: Wiley Interscience; 1994. p. 1-392 - 5.
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