Electron Paramagnetic Resonance in Modern Carbon-Based Nanomaterials

Dariya Savchenko, Abdel Hadi Kassiba, Dariya Savchenko, Abdel Hadi Kassiba

• Publisher: Bentham Science Publishers
• Year: 2018
• eBook ISBN:
  9781681086934
• Topic: Physical Sciences
• Subtopic: Analytic Chemistry

This volume presents information about several topics in the field of electron paramagnetic resonance EPR study of carbon-containing nanomaterials. It introduces the reader to an array of experimental and theoretical approaches for the analysis of param

Fundamentals of Electron Paramagnetic Resonance in Modern Carbon-based Materials

Sushil K. Misra^*

Department of Physics, Concordia University, Montreal, H3G 1M8, Canada

Abstract

The advantages of using multifrequency Electron Paramagnetic Resonance (EPR) in studying carbon-based materials are discussed. The details of designing continuous-wave EPR spectrometers operating at different frequencies are presented. Designs of CW and pulse Electron Nuclear Double Resonance (ENDOR) spectrometers, which are very important techniques for studying precisely hyperfine interactions and local environment of paramagnetic ions in carbon-based materials are included. Analysis of EPR spectra, spin Hamiltonians, EPR lineshapes, evaluation of spin-Hamiltonian parameters, and simulation of single-crystal and powder spectra are also explained. A short review of carbon-based materials studied by EPR is given.

Keywords: Carbon-based materials, Continuous Wave EPR, Davies ENDOR, Electron spin echo (ESE), Electron Spin Echo Envelope Modulation (ESEEM), Evaluation of spin Hamiltonian parameters, Electron Nuclear Double Resonance (ENDOR), EPR, EPR lineshape, EPR spectrometer, High-frequency spectrometers, Hyperfine interaction, Hyperfine Sublevel Correlation Spectroscopy (HYSCORE), Mims ENDOR, Pulse EPR, Pulse ENDOR, Simulation of EPR spectrum, Spin Hamiltonian, Zeeman effect.

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^* Corresponding author Sushil K. Misra: Department of Physics, Concordia University, Montreal, H3G 1M8, Canada ; Tel: [phone]; E-mail: [email protected]

ELECTRON ZEEMAN EFFECT: EPR RESONANCE CONDITION

In electron paramagnetic resonance (EPR), one observes the resonant absorption of microwave (mw) energy by an unpaired electron making a transition from a lower-energy state to a higher-energy state in the presence of an external magnetic field (The term EPR will be used throughout this chapter, although electron spin resonance (ESR) and electron magnetic resonance (EMR) are also used in the literature). These energy levels are due to the interaction of the electronic magnetic moment with the applied external magnetic field. An unpaired electron is equivalent to a small bar magnet due to its magnetic moment.

If it is aligned with B_ext, then its energy is lower than when it is aligned opposite to the direction of B_ext, as shown in Fig. (1). This effect is called the Zeeman Effect.

The unpaired electron possesses the spin 1/2, so its lower and higher energy states are designated by the electronic magnetic quantum numbers M_S = –1/2 and M_S = +1/2, respectively. Then expressed for the two values of M_S the energies E of an unpaired electron in an external magnetic field, B_ext, are:

(1)

where, the dimensionless constant, g, termed as g-factor, is expressed in terms of the gyromagnetic ratio, γ, as γ = gμ_B/ħ, where μ_B is the Bohr magneton (=9.274 × 10^-24 J/T; 1 Tesla [T] = 10.000 Gauss) and ħ is the reduced Plank’s constant (= h/2π, with h = 6.626 x 10^-34 J×s being Planck’s constant).

Fig. (1))
Lower (left) and higher (right) possible orientations of an unpaired electron’s magnetic moment in the external magnetic field, B_ext (Adapted from [1] with the Permission from John Wiley and Sons).

Under the action of an oscillating mw radiation of frequency υ₀ in Hertz, the resonance condition is satisfied when

(2)

where, B₀ = hυ₀/gμ_B, so that the energy level separation between the two energy levels represented by M_S = ±1/2, is equal to hυ₀. In that case, resonant absorption of mw radiation will take place for B_ext = B₀. This is shown in Fig. (2).

Fig. (2))
A plot showing the splitting due to Zeeman effect by the external magnetic field B_ext (neglecting hyperfine splitting and higher order zero-field splitting terms) and resonant absorption of mw radiation as the magnetic field is swept; adapted from [1] with the Permission from John Wiley and Sons).

HYPERFINE SPLITTING

The energy of the unpaired electron is influenced by its local surrounding. For instance, if there is a nucleus possessing magnetic moment near an unpaired electron, the magnetic field seen by the unpaired electron at its site would change due to the interaction between the electron and nuclear spin, known as hyperfine interaction (HFI) [2]. In that case, the external magnetic field required to satisfy the resonance condition given by eq. (2) will shift from B₀ accordingly. Therefore, if the effective local magnetic effect, B₁, depending on the HFI constant, of the nucleus on the unpaired electron is in the direction of B_ext, the resonance will occur at B_ext < B₀, and if B₁ opposes B_ext at the location of the unpaired electron, the absorption will occur at B_ext > B₀, for a given υ₀ (more details on HFI terms in the spin Hamiltonian are given below).

EPR LINE SHAPES

There are three types of line shapes, i.e. EPR absorption line intensity versus the magnetic field, usually observed in EPR. They are (i) Lorentzian, (ii) Gaussian, and (iii) Dysonian. These line shapes are expressed as:

(3)

(4)

and

(5)

respectively, where y is the line intensity; x is the magnetic field; x₀ is the resonance field; α is the fraction of the dispersion component added into the absorption signal for Dysonian line shape [3], and Δx is the linewidth. One obtains for the first-derivative absorption signal an expression, which is proportional to Y’_max(ΔB_pp)², where 2Y’_max is the amplitude of the peak-to-peak derivative, whereas ΔB_pp is the peak-to-peak linewidth.

When there exists superposition of many components which differ f...

Table of contents

• Welcome
• Table of Contents
• Title
• BENTHAM SCIENCE PUBLISHERS LTD.
• FOREWORD
• PREFACE
• List of Contributors
• Fundamentals of Electron Paramagnetic Resonance in Modern Carbon-based Materials
• Resolution of EPR Signals in Graphene-based Materials from Few Layers to Nanographites
• Study of Electron Spin Lifetime of Conducting Carbon Nanomaterials
• EPR Spectroscopy on Double-Walled and Multi-Walled Carbon Nanotube Polymer Composites
• Impact of Point Defects on Graphene Oxide and Carbon Nanotubes: Study of Electron Paramagnetic Resonance Spectroscopy
• Electron Spin Resonance Spectroscopy of Single-Walled Carbon-Nanotube Thin-Films and their Transistors
• Characterizing the Nature of Surface Radicals in Carbon-Based Materials, Using Gas-Flow EPR Spectroscopy
• Application of the Two-Temperature EPR Measurement Method to Carbonaceous Solids
• Paramagnetic Defects and Impurities in Nanodiamonds as Studied by Multi-frequency CW and Pulse EPR Methods
• EPR and FMR of SiCN Ceramics and SiCN Magnetic Derivatives
• CW and Pulse EPR Study of Paramagnetic Centers in Silicon Carbide Nanomaterials
• Size-dependent Effects in Silicon Carbide and Diamond Nanomaterials as Studied by CW and Pulse EPR Methods
• Paramagnetic Defects in Amorphous Hydrogenated Silicon Carbide and Silicon Carbonitride Films