Page 121 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN005E-212 June 15, 2001 20:32

332 Electron Spin Resonance

magnetic energy levels associated with different orienta-
tions of an electron spin in an atom or a molecule, gen-
erally in an external magnetic field. Measurement of the
allowed transitions between the electron magnetic energy
levels produces a spectrum of an atomic or molecular sys-
tem with net electron spin angular momentum. Generally
FIGURE 1 Energy-level diagram for ESR.
such systems are defined as those having one or more
unpaired electrons. Analysis of the electron spin reso- −24
nance spectrum can give information about the identifica- value of 9.27×10 J/T. This spin Hamiltonian operates
tion of the species, the geometric structure, the electronic only on spin wave functions and not on orbital wave func-
structure, and the internal or overall rotational or transla- tions that are commonly associated with electronic energy
tional motion of the species. The most common types of levels. For an electron there are two spin wave functions,
systems studied are free radicals, which can be regarded typically denoted by α and β, which are characterized by
1 ✥
1 ✥
✥
as atoms or molecules containing one unpaired electron, + h and − h where h is Planck’s constant divided by 2π
2
2
and transition-metal and rare-earth ions. The specificity and gives the unit of spin angular momentum. The two en-
of electron spin resonance spectroscopy for only species ergy levels associated with an electron in a magnetic field
1
1
containing unpaired electrons is particularly valuable for are thus given by + gβH and − gβH. The difference
2
2
the study of chemical reaction intermediates. between these two energy levels is gβH, so that the tran-
sition energy is given by h ν = gβH. This basic electron
spin resonance transition is illustrated in Fig. 1.
I. BASIC PRINCIPLES Typically, electron magnetic resonance is carried out in
a magnetic field of about 3000 G (gauss) or 0.3 T (tesla).
In general, the energy of a system or, more specifically, This corresponds to an energy absorption frequency of
of a molecule depends on momentum. The kinetic energy about 9 GHz. This frequency is in the microwave range.
of a molecule is proportional to the square of the linear As for any spectral transition, the number of systems or
momentum, and the rotational energy of the molecule is electrons in the upper and lower energy states at thermal
proportional to the square of the rotational or angular mo- equilibrium is given by a Boltzmann distribution.
mentum. An isolated electron can be regarded as a point
particle that has no classical angular momentum. How-
ever, experimentally it is found that isolated electrons in II. EXPERIMENTAL ASPECTS
a magnetic field do absorb a quantitized amount of en-
ergy, which means that they must have at least two energy Figure 2 shows a block diagram of a typical electron spin
levels. These are not translational energy levels, because resonance (ESR) spectrometer. It can be seen that this
the amount of energy absorbed does not depend on the diagram is analogous to that for an optical absorption
kinetic energy of the electron. However, the magnitude spectrometer, consisting of a source of electromagnetic
of the energy absorbed does depend on the magnitude of optical radiation, a sample cavity, and a detector of the op-
the magnetic field to which the electrons are exposed. As tical radiation intensity. In the block diagram of the ESR
an explanation of the existence of these magnetic energy spectrometer, the microwave irradiation is produced by a
levels,itispostulatedthatanelectronhasanintrinsicangu- special microwave tube called a klystron or a solid-state
lar momentum called spin angular momentum. When this device called a Gunn diode. The microwaves are transmit-
spin angular momentum interacts with a magnetic field, ted through a rectangular waveguide or through a special
two different energy levels are produced whose difference coaxial cable to an isolator, which is a ferrite device al-
accounts for the absorption of energy by the unpaired elec- lowing microwaves to travel in only one direction. This
tron system. component is used so as to prevent reflection of the mi-
The Hamiltonian energy operator for the electron spin crowaves back into the klystron tube or Gunn diode. The
transition we have just discussed is given by microwaves then pass through a device called an attenua-
tor, which simply controls the intensity of the microwaves
spin = gβS · H, (1)
and consists of a resistive but electrically conducting ele-
where spin is the spin Hamiltonian energy operator; S ment that penetrates to different extents into a waveguide.
is the spin angular momentum; H is the magnetic field; Although not shown, there also are devices available to
gβ is a proportionality constant, where g = 2.0023 and is shift the phase of the microwaves if that is necessary. The
called the g factor or spectroscopic splitting factor, which microwaves then pass into a circulator, which is a ferrite
is dimensionless; and β is the Bohr magneton, which has a device that routes the microwaves in one port and out an