Easy-to-follow guide helps you take full advantage of EPR spectroscopy’s capabilities

Electron Paramagnetic Resonance: A Practitioner’s Toolkit serves as a practical guide that enables you to navigate through and make sense of the complex maze of electron paramagnetic resonance (EPR) spectroscopy fundamentals, techniques, and applications. The first half of this book is dedicated to explaining the core principles of EPR spectroscopy, using clear, easy-to-follow explanations and examples while avoiding complex physics and mathematics. The second half of the book focuses on applications, including problem-solving strategies for such fields as biology, medicine, material science, chemistry, physics, and radiation effects on matter.

Carefully edited by two experienced EPR scientists, this book features a team of eighteen expert authors. Their contributions are based not only on a thorough examination and analysis of the primary literature, but also on their own firsthand experience in research and applications. As a result, the book is filled with practical advice, tips, and cautions addressing such issues as:

• Choosing the right experiment

• Selecting experimental parameters and sample size

• Avoiding setbacks and pitfalls

• Simulating the spectra

With its straightforward explanations and clear examples, this book is just what researchers need to take full advantage of EPR spectroscopy’s tremendous capabilities. It is particularly recommended for those interested in applications to chemistry, biology, medicine, and material science.

Marina Brustolon is a full professor in physical chemistry at the Università degli Studi di Padova in Italy.

Elio Giamello is a full professor in inorganic chemistry at the Università degli Studi di Torino in Italy.

Principles and Applications of Electron Paramagnetic Spectroscopy

John Wiley & Sons

Copyright © 2009 John Wiley & Sons, Inc.
All right reserved.
ISBN: 978-0-470-25882-8

Chapter One

Introduction to Electron Paramagnetic Resonance

CARLO CORVAJA

Dipartimento di Scienze Chimiche, Universita` di Padova, Via Marzolo 1, 35131 Padova, Italy

Electron paramagnetic resonance (EPR), which is also called electron spin resonance (ESR), is a technique based on the absorption of electromagnetic radiation, which is usually in the microwave frequency region, by a paramagnetic sample placed in a magnetic field. EPR and ESR are synonymous, but the acronym EPR is used in this book. The absorption takes place only for definite frequencies and magnetic field combinations, depending on the sample characteristics, which means that the absorption is resonant.

The first EPR experiment was performed more than 60 years ago in Kazan (Tatarstan), which is now in the Russian Federation, by E. K. Zavoisky, a physicist who used samples of Cu[Cl.sub.2]. 2[H.sub.2]O, a radiofrequency (RF) source operating at 133 MHz, and a variable magnetic field operating in the range of a few millitesla and provided by a solenoid. More than five decades from the first experiment the technique has progressed tremendously and EPR has a broad range of applications in the fields of physics, chemistry, biology, earth sciences, material sciences, and other branches of science. Modern EPR spectrometers are much more complex than those used for demonstrating the phenomenon; they have much higher sensitivity and resolution and can be used with a large number of samples (crystalline solids, liquid solutions, powders, etc.) in a broad range of temperatures.

1.1 CHAPTER SUMMARY

The aim of this chapter is to provide the reader with the basic information about the phenomenon of electron magnetic resonance and the ways to observe it and to record an EPR spectrum. EPR spectra of very simple molecular systems will be described together with the properties that influence the shape of the spectra and the intensity of the spectral lines. Moreover, it will be anticipated how the parameters characterizing the spectrum are related to molecular structure and dynamics. The approach will be as simple and intuitive as possible within the constraints of a rigorous treatment. Details on instrumentation, types of paramagnetic species studied, specific characteristics of EPR in solids and in solution, and theory are the subjects of the ensuing chapters. The second part of the book will consider applications to the investigation of complex chemical and biological systems and the improvements of the technique suitable for them.

An illustration of the spin properties of a single electron and its behavior in a magnetic field will be presented first, followed by a short discussion about the behavior of an electron spin when it is confined in a molecule, as well as when it interacts with one or several nuclear spins.

The macroscopic observation of EPR requires a collection of many electron spins the properties for which will be treated in a semiclassical way, leaving to more advanced EPR descriptions the quantum mechanical density matrix method. (You can find, e.g., a short account of the density matrix method applied to ensembles of spins in appendix A9 in the Atherton book in the Further Reading Section.) However, a quantum mechanical description is necessary to a deeper understanding of complex experiments, in particular pulse EPR experiments. A short introduction to quantum mechanics formalism will be presented at the end of this chapter. The concepts of spin-lattice (longitudinal) and spin-spin (transverse) relaxation processes will be introduced, and how the rate of these processes influences the spectra will be anticipated. Chapter 5 describes how the relaxation rates can be measured by pulsed EPR methods.

The presence of a second electron spin in the investigated paramagnetic system will be considered briefly. A second electron spin introduces the electron dipolar interaction, which constitutes a new important term in the energy. Chapters 3 and 6 contain more information on paramagnetic species with two or more unpaired electrons.

Analogies and differences with respect to the related phenomena of nuclear magnetic resonance (NMR), involving nuclear spins, will be provided when appropriate.

1.2 EPR SPECTRUM: WHAT IS IT?

The EPR spectrum is a diagram in which the absorption of microwave frequency radiation is plotted against the magnetic field intensity. The reason why the magnetic field is the variable, instead of the radiation frequency as it occurs in other spectroscopic techniques (e.g., in recording optical spectra), will be explained in Chapter 2. There are two methods to record EPR spectra: in the first traditional method, which is called the continuous wave (CW) method, low intensity microwave radiation continuously irradiates the sample. In the second method, short pulses of high power microwave radiation are sent to the sample and the response is recorded in the absence of radiation (pulsed EPR). This chapter is mainly focused on the CW method, and pulsed EPR is treated in Chapter 5. In CW spectra, for technical reasons explained in Chapter 2 (2.1.4), the derivative of the absorption curve is plotted instead of the absorption itself. Therefore, an EPR spectrum is the derivative of the absorption curve with respect to the magnetic field intensity.

Microwave absorption occurs by varying the magnetic field in a limited range around a central value [B.sub.0], and the EPR spectrum in most cases consists of many absorption lines. The following main parameters and features characterize the spectrum: the positions of the absorptions, which are the magnetic field values at which the absorptions take place; the number, separation, and relative intensity of the lines; and their widths and shapes. All of these parameters and features are related to the structure of the species responsible for the spectrum, to their interactions with the environment, and to the dynamic processes in which the species are involved. This chapter will address these issues.

1.3 THE ELECTRON SPIN

Elementary particles such as an electron are characterized by an intrinsic mechanical angular momentum called spin; that is, they behave like spinning tops. Angular momentum is a vector property that is defined by the magnitude or modulus (the length of the vector used to represent the angular momentum) and by the direction in space. However, because an electron is a quantum particle, the behavior of its spin is controlled by the rules of quantum mechanics. For a first approach to the magnetic resonance phenomenon, it is sufficient to know that the electron spin can be in two states, usually indicated by the first letters of the Greek alphabet [alpha] and [beta]. These states differ in the orientation of the angular momentum in space but not in the magnitude of the angular momentum, which is the same in the [alpha] and [beta] states. The spin vector is indicated by S and the components along the x, y, z axes of a Cartesian frame by [S.sub.x], [S.sub.y], [S.sub.z], respectively. The angular momenta of quantum particles are of the order of h (Planck constant h divided by 2[pi]). Magnetic moments are usually represented in h units, and in these units the magnitude or modulus of S is

|S| = [square root of (S(S + 1)] (1:1)

where S = 1/2 is the electron spin quantum number; therefore, |S| = [square root of (3/4)]. The usual convention is to consider the a and b electron spin states as those having definite components [S.sub.z] along the z axis of the Cartesian frame. For an electron spin, quantum mechanics requires that [S.sub.z] be in h units of either 1/2 ([alpha] state) or 2 1/2 ([beta] state). The components along the axes perpendicular to z are not defined in the sense that they cannot be determined (another requirement of quantum mechanics), and in the a and [beta] states they could assume any value in the range of – 1/2 to 1/2. In the absence of any particular preferential direction in the space, connected with possible interactions of the electron spin with its environment, any choice for the direction in space of the z axis is allowed. As long as this space isotropy condition holds, the a and [beta] electron spin states have the same energy (Fig. 1.1) and they are said to be degenerate. This is not the case if the electron spin is placed in a magnetic field.

1.4 ELECTRON SPIN IN A MAGNETIC FIELD (ZEEMAN EFFECT)

In EPR a crucial point to be considered is that a magnetic moment [[mu].sub.e] is always associated with the electron spin angular momentum, where [[mu].sub.e] is proportional to S, meaning that [[mu].sub.e] and S are vectors parallel to each other. They have opposite directions because the proportionality constant is negative. The latter is written as the product of two factors g and [[mu].sub.B]:

[[mu].sub.e] = g [[mu].sub.B]S (1:2)

where g is a number called the Land factor or simply the g factor. For a free electron g = 2.002319 and [[mu].sub.B] = -|e|h/4[pi][m.sub.e] = [9.27410.sup.-24] J[T.sup.-1], where [m.sub.e] is the electron mass; e is the electron charge; h = 6.626 x [10.sup.-34] Js is the Planck constant; and [[mu].sub.B] is the atomic unit of the magnetic moment, which is called the Bohr magneton. Because [[mu].sub.B] <0, to avoid confusion about the sign, the absolute value of [[mu].sub.B] will be used in several equations. The existence of a magnetic moment associated with the electron spin is the reason for having an energy separation between the [alpha] and [beta] electron spin states when the electron is in the presence of a magnetic field. Suppose we apply a constant magnetic field B to an electron spin. Because the energy of a magnetic moment [[mu].sub.e] is given by the scalar product between [[mu].sub.e] and B, the electron spin energy will depend on the orientation of [[mu].sub.e] with respect to B:

E = [[mu].sub.e] B = g|[[mu].sub.B]|S B (1:3)

The dot product reduces to a single term if the direction of B coincides with one of the axes respect to which the B and S are represented. The choice of the reference frame is arbitrary, and it can be chosen in such a way that the z axis is along the direction of B. In this case the equation for the energy becomes

E = g|[[mu].sub.B]|[B.sub.0][S.sub.z] (1:4)

where [B.sub.0] is the magnetic field intensity.

If one takes into account that the electron spin can be in two states, either [alpha] or [beta], in which the z component of the spin is 1/2 and -1/2, respectively, in the presence of a magnetic field the electron spin energy could assume only the two values,

E = (1/2)g|[[mu].sub.B|[B.sub.0] (1:5)

where the positive sign refers to the a state and the negative one to the [beta] state.

The splitting of the electron spin energy level into two levels in the presence of a magnetic field is called the Zeeman effect, and the interaction of an electron magnetic moment with an external applied magnetic field is called the electron Zeeman interaction. The Zeeman effect is represented graphically in Fig. 1.2.

1.5 EFFECT OF ELECTROMAGNETIC FIELDS

An electron spin in the [beta] state, which is the low energy state, can absorb a quantum of electromagnetic radiation energy, provided that the energy quantum hv coincides with the energy difference between the [alpha] and [beta] states:

hv = [E.sub.[alpha]] – [E.sub.[beta]] = g|[[mu].sub.B]|[B.sub.0] (1:6)

where v is the radiation frequency. Equation 1.6 is the fundamental equation of EPR spectroscopy.

In a 3.5-T magnetic field, which is the standard magnetic field intensity used in many EPR spectrometers, for g = 2.0023, Equation 1.6 gives n = 9.5 GHz. This radiation frequency is in the microwave X-band region (8-12 GHz). The EPR spectrometers operating in this frequency range are called X-band spectrometers.

Other regions of higher microwave frequencies used in commercial EPR spectrometers are Q-band (~34 GHz) and W-band (95 GHz). Spectrometers operating at frequencies higher than 70 GHz are considered as high field/high frequency spectrometers. See Chapter 2 (2.2.5) for a general introduction to multifrequency EPR. Applications of high field/high frequency EPR are described in Chapters 6 and 12.

For the spin system to absorb the radiation energy, the oscillating magnetic field [B.sub.1] associated with the electromagnetic radiation should be in the plane xy, which is perpendicular to the static Zeeman field [B.sub.0]. In other words, the radiation should be polarized perpendicular to [B.sub.0].

An electron spin in the [alpha] state cannot absorb energy because there are no allowed states at higher energy. However, the presence of an oscillating magnetic field of proper frequency corresponding to Equation 1.6 induces a transition from the [alpha] state to the [beta] state with loss of energy and emission of a radiation quantum hv. This process is called stimulated emission, and it is just the opposite of the absorption. The spontaneous decay of an isolated spin to the lower energy state in the absence of radiation, with emission of microwave radiation (spontaneous emission), is a process occurring with negligible probability.

In conclusion, an isolated electron spin placed in a static magnetic field [B.sub.0] and in the presence of a microwave oscillating magnetic field [B.sub.1] perpendicular to [B.sub.0] undergoes transitions from the low energy level state [beta] to the upper one [alpha], and vice versa. The net effect is zero because absorption and stimulated emission compensate each other. The next section will show that electron spins are never completely isolated, and the behavior of a collection of many electron spins is different.

1.6 MACROSCOPIC COLLECTION OF ELECTRON SPINS

In the usual experimental setup one considers samples of many electron spins, their number being on the order of [10.sup.10] or higher. Moreover, these electron spins are not independent, interacting with each other and with their environment. Furthermore, electron spins are not free; they are confined in atomic or molecular systems. The latter aspects will be considered later.

The electron spins of an ensemble are statistically distributed in the [alpha] and [beta] states. Because these states are equivalent in the absence of a magnetic field, for [B.sub.0] = 0 half of the spins are a spins and half are [beta] spins. In these conditions the z component of the total angular momentum is zero, as are also the components along any other direction. In fact, all directions in space are equivalent. The situation changes in the presence of a magnetic field [B.sub.0] if the spin ensemble is allowed to interact with its environment (the “lattice”). As learned in the previous section, if [B.sub.0] [not equal to] 0, the [alpha] and [beta] states do not have the same energy. In thermal equilibrium with the lattice the spins distribute between [alpha] and [beta] states in such a way as to be in a small excess in the lower energy level ([beta] state). The ratio between the number (N) of [alpha] spins and the number of [beta] spins depends on the temperature. It is given by the Boltzmann distribution law:

[N.sub.[alpha]]/[N.sub.[beta]] = exp (-g|[[mu].sub.B]|[B.sub.0]/ [k.sub.B]T) (1:7)

where [k.sub.B] is the Boltzmann constant, which is equal to 1.3806 x [10.sup.-23] J [K.sup.-1]; and T is the absolute temperature of the lattice.

At room temperature (300K) and for magnetic fields on the order of 0.3 T (X-band spectrometer), g|[[mu].sub.B][B.sub.0] [much less than] [k.sub.B]T and the exponential can be expanded in series, retaining only the linear term. The approximate population ratio becomes

[N.sub.[alpha]]/[N.sub.[beta]] = 1 – g|[[mu].sub.B]|[B.sub.0]/[k.sub.B]T (1:8)

This approximation is quite good, unless the spin system is at very high field or at very low temperature. According to Equation 1.8, at room temperature in the magnetic field of an X-band spectrometer there is an excess of [beta] spins over the a spins of 1/1000. This small excess is enough for the microwave absorption to overcome the emission and to make possible the observation of an EPR absorption signal. In fact, a microwave field induces transitions from [beta] to [alpha], and the reverse one from [alpha] to [beta], in a number proportional to the number of spins in the initial state.

(Continues…)

Excerpted from Principles and Applications of Electron Paramagnetic Spectroscopy Copyright © 2009 by John Wiley & Sons, Inc.. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.