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SHULAMITH SCHLICK, DSc, is a Professor of Physical and Polymer Chemistry in the Department of Chemistry and Biochemistry, University of Detroit Mercy. One of the foremost authorities in the field of polymer research, and the editor of one previous book, Dr. Schlick has held visiting professorships and appointments worldwide and has authored over 200 scientific articles and book chapters.

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A definitive work on ESR and polymer science by today's leading authorities

The past twenty years have seen extraordinary advances in electron spin resonance (ESR) techniques, particularly as they apply to polymeric materials. With contributions from over a dozen of the world's top polymer scientists, Advanced ESR Methods in Polymer Research is the first book to bring together all the current trends in this exciting field into one comprehensive reference.

Part I establishes the fundamentals of ESR, from experimental techniques to data analysis, and serves as a valuable overview for the beginning ESR student. Part II introduces the broad range of ESR applications to polymeric systems, including living radical polymerization, block copoly-mers, polymer solutions, ion-containing polymers, polymer lattices, membranes in fuel cells, degradation, polymer coatings, dendrimers, and conductive polymers. By exposing readers to the great potential of ESR, the authors hope to encourage more extensive application of these methods.

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Advanced ESR Methods in Polymer Research

John Wiley & Sons

Chapter One

Gunnar Jeschke Max Planck Institute for Polymer Research, Mainz, Germany

Shulamith Schlick University of Detroit Mercy, Detroit, Michigan

Contents

1. Introduction 3 2. Fundamentals of Electron Spin Resonance Spectroscopy 4 2.1. Basic Principles 4 2.2. Anisotropic Hyperfine Interaction and g-Tensor 10 2.3. Isotropic Hyperfine Analysis 12 2.4. Environmental Effects on g- and Hyperfine Interaction 12 2.5. Accessibility to Paramagnetic Quenchers 13 2.6. Line Shape Analysis for Tumbling Nitroxide Radicals 15 3. Multifrequency and High-Field ESR 16 4. Pulsed ESR Methods 18 Acknowledgments 22 References 22

1. INTRODUCTION

Electron spin resonance (ESR) is a spectroscopic technique that detects the transitions induced by electromagnetic radiation between the energy levels of electron spins in the presence of a static magnetic field. The method can be applied to the study of species containing one or more unpaired electron spins; examples include organic and inorganic radicals, triplet states, and complexes of paramagnetic ions. Spectral features, such as resonance frequencies, splittings, line shapes, and line widths, are sensitive to the electronic distribution, molecular orientations, nature of the environment, and molecular motions. Theoretical and experimental aspects of ESR have been covered in a number of books, and reviewed regularly.

Currently available textbooks and monographs are written for students and scientists that specialize in the development of ESR technique and its application to a broad range of samples. Nowadays, however, research groups are interested in a specific field of applications, such as polymer science, and apply more than one characterization method to the materials of interest. An introduction to ESR that targets such an audience needs to be shorter, less mathematical, and focused on application rather than methodological issues. This chapter is an attempt to provide such a short introduction on the application of ESR spectroscopy to problems in polymer science.

Organic radicals occur in polymers as intermediates in chain-growth and depolymerization reactions, or as a result of high-energy irradiation ([gamma], electron beams). Paramagnetic transition metal ions are present in a number of functional polymer materials, such as catalysts and photovoltaic devices. However, much of the modern ESR work in polymer science focuses on diamagnetic materials that are either doped with stable radicals as "spin probes", or labeled by covalent attachment of such radicals as "spin labels" to polymer chains. This chapter therefore treats the basic concepts that are required to understand ESR spectra of a broad range of organic radicals and transition metal ions, and describes more advanced concepts as applied to the most popular class of spin probes and labels: nitroxide radicals.

2. FUNDAMENTALS OF ELECTRON SPIN RESONANCE SPECTROSCOPY

2.1. Basic Principles

Spins are magnetic moments that are associated with angular momentum; they interact with external magnetic fields (Zeeman interaction) and with each other (couplings). In most cases, the Zeeman interaction of the electron spin is the largest interaction in the spin system (high-field limit). The electron Zeeman (EZ) interaction can generally be described by the Hamiltonian below,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where S is the spin vector operator, [B.sub.0] is the transposed magnetic field vector in gauss (G) or tesla (1 T = [10.sup.4] G), [.sub.e] is the Bohr magneton equal to 9.274 x [10.sup.-21] erg[G.sup.-1] (or 9.274 x [10.sup.-24] [JT.sup.-1]), and g is the g tensor. For a free electron, g is simply the number [g.sub.e] = 2.002319. The transition energy is then [DELTA]E = h]v.sub.mw] = [g.sub.e] [.sub.e][B.sub.0], where [B.sub.0] is the magnitude of the magnetic field. Typical values are [B.sub.0] [approximately equal to] 0.34 T (3400 G) corresponding to microwave (mw) frequencies of [approximately equal to] 9.6 GHz (X band), or [B.sub.0] [approximately equal to] 3.35 T corresponding to mw frequencies of [approximately equal to] 94 GHz (W band).

The g-value of a bound electron generally exhibits some deviation from [g.sub.e] that is mainly due to interaction of the spin with orbital angular momentum of the unpaired electron (spin-orbit coupling). Spin-orbit coupling is a relativistic effect that tends to increase with increasing atomic number of the nuclei that contribute atomic orbitals to the singly occupied molecular orbital. Therefore, g-values deviate more strongly from [g.sub.e] for transition metal complexes than for organic radicals. As the orbital angular momentum is quenched in the ground state of molecules, spin-orbit coupling comes about only by admixture of excited orbitals. Such admixture is stronger for low-lying excited states, which are relevant, for example, if the unpaired electron has high density at an oxygen atom. Oxygen-centered organic radicals thus tend to have higher g-values than carbon-centered ones.

As the orbital angular momentum relates to a molecular coordinate frame and the spin is quantized along the magnetic field (z axis of the laboratory frame), the g-value depends on the orientation of the molecule with respect to the field. This anisotropy can be described by a second rank tensor with three principal values, [g.sub.x], [g.sub.y], and [g.sub.z]. The corresponding principal axes define the molecular frame. In fluid solutions, molecules tumble with a rotational diffusion rate that is much higher than the differences of the electron Zeeman frequencies between different orientations. In this situation, the g-value is orientationally averaged and only its isotropic value [g.sub.iso] = ([g.sub.x] + [g.sub.y] + [g.sub.z])/3 can be measured. A good overview of isotropic g-values of organic radicals can be found in Ref. 23; Ref. 5 collects information on g tensors for transition metal complexes.

The real power of ESR spectroscopy for structural studies is based on the interaction of the unpaired electron spin with nuclear spins. This hyperfine interaction splits each energy level into sublevels and often allows the determination of the atomic or molecular structure of species containing unpaired electrons, and of the ligation scheme around paramagnetic transition metal ions. For a system with m nuclear spins (identified by index k) and a single electron spin, which may be larger than one-half as explained below, the hyperfine Hamiltonian is given in Eq. 2,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where the [I.sub.k] are nuclear spin vector operators and the [A.sub.k] are hyperfine tensors in frequency units (Hz). Each hyperfine tensor is characterized by three principal values [A.sub.x], [A.sub.y], and [A.sub.z] and by the relative orientation of its principal axes system with respect to the molecular frame defined by the g-tensor. This relative orientation is most easily defined by three Euler angles [alpha], , [gamma], which correspond to a sequence of rotations about the z axis (by angle [alpha]), the new y' axis (by angle ), and the final z" axis (by angle [gamma]); these rotations transform the principal axes frame of the hyperfine tensor into that of the g-tensor. The relative orientation is often given as direction cosines, which are the coordinates of unit vectors along the directions of the hyperfine principal axes given in the coordinate frame of the g-tensor.

Only the isotropic value [A.sub.iso] = ([A.sub.x] + [A.sub.y] + [A.sub.z])/3 can be measured in fluid solutions, and is due to the Fermi contact interactions of electrons that reside in an s orbital of the nucleus under consideration. The contribution of a single orbital is proportional to the spin population (spin density) in that orbital, to the probability density [|[[PSI].sub.0]|.sup.2] of the orbital wave function at its center (inside the nucleus), and to the nuclear g-value, [g.sub.n]. To a very good approximation, the hyperfine couplings for different isotopes of the same element thus have the same ratio as the [g.sub.n] values.

Purely anisotropic contributions ([A.sub.x] + [A.sub.y] + [A.sub.z] = 0) to the hyperfine coupling result from spin density in p, d, or f orbitals on the nucleus and from the dipole-dipole interaction T between the electron and nuclear spin. If the electron spin is confined to a region that is much smaller than the electron-nuclear distance [r.sub.en], both spins can be treated as point dipoles and the magnitude of T is proportional to [r.sub.en.sup.-3]. In this case, T has axial symmetry and its principal values are given by [T.sub.x] = [T.sub.y] = -T and [T.sub.z] = 2T. Furthermore, if the spin density in p, d, and f orbitals on that nucleus is negligible, as is the case for protons ([sup.1]H), the measurement of the hyperfine anisotropy can provide the electron-nuclear distance [r.sub.en]. Any spin density at the nucleus under consideration is negligible if this nucleus is located in a neighboring molecule and does not interact (by van der Waals or hydrogen bonding) with a nucleus on which much spin density is located. Intermolecular distances larger than [approximately equal to] 0.3 nm can thus be inferred from hyperfine couplings.

For nuclei with significant hyperfine interaction, the other interactions of the nuclear spin also need to be considered. The nuclear Zeeman (NZ) interaction of these spins with the external magnetic field is described in Eq. 3.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Nuclear spins with I > 1/2 have an electric quadrupole moment that interacts with the quadrupole moment of the charge distribution around the nucleus. The Hamiltonian for this nuclear quadrupole (NQ) interaction is given in Eq. 4,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [Q.sub.k] are the traceless ([Q.sub.x] + [Q.sub.y] + [Q.sub.z] = 0) nuclear quadrupole tensors. Because the tensor is traceless, this interaction is not detected in fluid media.

Both the nuclear Zeeman and nuclear quadrupole interaction do not depend on the magnetic quantum number [m.sub.S] of the electron spin. As the selection rule for ESR transitions is given by Eq. 5,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [m.sub.I] is the nuclear spin quantum number, these interactions do not make a first-order contribution to the ESR spectrum. In many cases, they can thus be neglected in spectrum analysis. This situation is illustrated in Fig. 1 for a nitroxide in which the nuclear spin I = 1 of the [sup.14]N atom is coupled to the electron spin S = 1/2 that resides mainly in the [p.sub.z] orbitals on the N and O atom. The hyperfine coupling causes a splitting of each of the electron spin levels ([m.sub.S] = -1/2 and [m.sub.S] = + 1/2) into three sublevels. When a constant microwave frequency [v.sub.mw] is irradiated and the magnetic field is swept, three resonance transitions are observed (Fig. 1a). The nuclear Zeeman interaction shifts both [m.sub.I] = +1 sublevels to lower and both [m.sub.I] = -1 sublevels to higher energy, but does not influence the resonance fields where the splitting between the levels with different [m.sub.S] and the same [m.sub.I] matches the energy of the mw quantum (Fig. 1b).

More generally, the higher sensitivity of ESR experiments can be used for the detection of NMR frequencies by applying both resonant mw and resonant radio frequency (rf) irradiation to the spin system. Such electron nuclear double-resonance (ENDOR) experiments are discussed in Chapter 2.

Transition metal ions can have several unpaired electrons when they are in their high- spin state; examples are Cr(III) (3[d.sup.3] configuration, S = 3/2), Mn(II) (3[d.sup.5], S = 5/2), and Fe(III) (3[d.sup.5], S = 5/2). The spins of these electrons are tightly coupled and have to be considered as a single group spin S > 1/2. Such an electron group spin also has an electric quadrupole moment. For historical reasons, the electron spin analog of the nuclear quadrupole interaction is termed zero-field splitting (ZFS) and is described by Eq. 6,

[[??].sub.ZFS] = h S D S (6)

where D is a traceless tensor. Therefore, the ZFS can be characterized by two parameters, D = 3[D.sub.z]/2 and E = ([D.sub.x] - [D.sub.y])/2, rather than by giving all three principal values. For axial symmetry E = 0, and for maximum nonaxiality E = D/3.

With the exception of transition metal ions at a site with cubic symmetry, the ZFS often exceeds the electron Zeeman interaction at magnetic fields < 1 T, sometimes even at the highest accessible fields (high-spin Fe(III)). In this situation, only the lowest lying doublet of spin states may be populated and only transitions within this doublet can be observed. It is convenient to describe such a doublet by an effective spin S'= 1/2. The ZFS of the group spin S > 1/2 then contributes to the effective g-tensor of the spin S' = 1/2. For example, X-band ESR spectra of high-spin Fe(III) in a situation with maximum nonaxiality of the ZFS (E = D/3) exhibit a sharp feature at g = 4.3. Note that unlike the normal g-tensor, the effective g-tensor may depend on the applied magnetic field.

For low concentrations of the paramagnetic centers, the electron spins can be considered isolated from each other, and only a single electron spin S appears in the Hamiltonian. In systems with a high concentration of paramagnetic transition metal ions, this situation can be achieved by diamagnetic dilution with transition ions of the same charge and similar radius and coordination chemistry. However, there are a number of systems that feature coupled electron spins, for example, binuclear metal complexes and biradicals. Any pair of electron spins [S.sub.k] and [S.sub.l] in such a system interacts through space by dipole-dipole coupling, which is analogous to the dipolar part T of the hyperfine coupling. The Hamiltonian of the electronic dipole-dipole (DD) coupling is given by Eq. 7,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where the [D.sub.kl] are the traceless dipole-dipole tensors. If the two electron spins are far apart, the coupling can be described by a point-dipole approximation in which [D.sub.kl] is an axial tensor with principal values [D.sub.z,kl] = 2d and [D.sub.x,kl] = [D.sub.y,kl] = -d. As d is inversely proportional to the cube of the distance [r.sub.kl] between the two spins, a measurement of this coupling can thus yield the spin-spin distance. Such measurements are discussed in more detail in Chapter 2.

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