Principles and Applications of Electron Paramagnetic Resonance Spectroscopy
Other Course , Prof. Ranjan Das
150 students enrolled
Remembering the Masters: From Zeeman to Zavoisky:Zeemans observation of splitting of spectral lines; the difficulty of explaining the origin of Zeeman effect; Bohr model of hydrogen atom; Paulis exclusion principle; Stern-Gerlach experiment; Uhlenbeck and Goudsmits idea of spinning motion of electron and its initial dismissal by Pauli and Lorentz; Intrinsic magnetic moment and angular momentum of electron; Zavoiskys observation of electron paramagnetic resonance;Introduction to EPR spectroscopy:The Zeeman effect; Magnetic moment of an electron due its spin and orbital angular momenta; Combination of angular momenta and explanation of fine structures in atomic spectra; Magnetic moment in a magnetic field; Zeeman splitting of energy levels; Electron Zeeman vs nuclear Zeeman effect; Magnetic resonance spectroscopy; Resonance condition; Field-swept vs frequency-swept EPR spectra; Observation of hyperfine lines in several organic free radicals and transition metal complexes and the existence of electron-nuclear hyperfine interaction;Electron-Nuclear Hyperfine Interaction:Understanding the electron-nuclear hyperfine interaction; Hydrogen atom; Hydrogen molecule ion (H2+); Nuclear spin-degeneracy and relative intensity of hyperfine lines; EPR spectra of benzosemiquinone anion radical, methyl radical; Pascal triangle for several equivalent spin- nuclei; Hyperfine lines due nuclear spin I = 1; EPR spectrum of TEMPOL free radical - Hyperfine lines due nuclear spin I > ; EPR spectra of copper diethyl dithio-carbamate complex containing naturally abundant and isotopically pure 63Cu nucleus; Linewidths and intensities of various hyperfine lines; EPR spectrum of di-vanadyl complex; Pascal-like triangle for several equivalent nuclei with I > ; EPR vs ESR EPR spectrum of singlet oxygen molecule; splittings due to coupling of orbital angular momentum with rotational angular momentum;Magnetic Moment in Magnetic Field:Review of vector algebra: Right-hand Cartesian coordinate system, scalars and vectors, vector addition and multiplication; Motion of a bar magnet in a magnetic field; Oscillation; Relation between the magnetic moment and orbital angular momentum of an electron; Bohr magneton; Lorentz force; Tesla vs Gauss - Motion of a bar magnet in a magnetic field, contd.; Oscillation vs precession; Time-dependence of the magnetic moment in a magnetic field; Gyromagnetic ratio; Larmor frequency; Effect of a small rotating magnetic field applied perpendicular to the Zeeman field; Condition for magnetic resonance;EPR Instrumentation:Recapitulation of the requirements of EPR transition; Comparison between a basic EPR spectrometer and an optical spectrometer; Microwave components waveguides, bends, twist; Different microwave frequencies and EPR spectrometers; Source of microwave klystron and Gunn oscillator; Klystron mode; Microwave cavity transmission and reflection type; Modes in a microwave cavity; Microwave oven; Perturbation of modes due to a sample; TE102 modes in a rectangular cavity; TE011 modes in a cylindrical cavity; Fixed frequency EPR spectrometer; Quality factor (Q) of a cavity and its importance in sensitivity of the spectrometer - Magnetic field and electromagnet; Helmholtz coil; Requirements on the homogeneity; Measuring the magnetic field Hall-effect Gaussmeter and NMR Gaussmeter; Microwave detector; Non-linearity and biasing of the detector; Coupling of microwave from waveguide to the cavity role of an iris and a tuning screw; Describing microwave power in relative unit (dB) and absolute unit (dBm) - A transmission-cavity EPR spectrometer; Microwave circulator; A reflection-cavity EPR spectrometer; Matching the microwave frequency to the resonance frequency of the cavity; Coupling the microwave from the waveguide to the cavity role of an iris and a tuning screw; Undercoupling, overcoupling and critically coupling of the cavity; Biasing the detector using a directional coupler; Use of attenuators and phase shifters in the spectrometer; Balancing the microwave bridge analogous to a Wheatstone bridge; Appearance of the EPR spectra positive or negative; Direct-detection EPR spectrometer; Q value and the response time of a direct-detection EPR spectrometer - Improving the sensitivity of the EPR spectrometer; Signal-to-noise ratio; Signal averaging; Principle of lock-in or phase-sensitive detection; Magnetic field modulation andphase-sensitive detection; EPR spectrum in first-derivative form; Second-derivative form of EPR spectrum; Factors deciding the sense of the derivative spectrum; Magnetic field modulation and side bands; Effect on the response time of the spectrometer; Automatic frequency control of the microwave source;Quantum Mechanical Description of EPR:Recapitulation of the classical view of EPR transition; Basics of quantum mechanics wave function, time-dependent and time-independent Schrdinger equations; Angular momentum and its allowed values; Stationary states in quantum mechanics; Magnetic moment in a Zeeman magnetic field; Allowed states and energies; Rotating magnetic field in the xy plane; First-order time-dependent perturbation calculations - First-order time-dependent perturbation calculations, contd; Time-dependent evolution of states; Transition probability; Resonance condition.
Introduction to Spin Relaxation:Absorption, spontaneous emission and stimulated emission processes; Need for relaxation processes in magnetic resonance spectroscopy; Phenomenological derivation of spin-lattice relaxation as an exponential process; Physical meaning of the spin-lattice and spin-spin relaxation processes; Role of the relaxation process in the appearance of EPR spectra;Theory of First-order EPR Spectra:Hamiltonian of hydrogen atom; Magnetic interactions and spin hamiltonian; Hamiltonian for Zeeman interaction; Hamiltonian for electron-nuclear dipolar interaction and its directional dependence; Hamiltonian for electron-nuclear isotropic hyperfine interaction; Importance of s-type of orbitals; Separating the total hamiltonian into a main unperturbed Hamiltonian and a perturbation hamiltonian - Zeroth order wavefunctions and energies of hydrogen atom; Splitting of energy levels due to electron Zeeman, nuclear Zeeman and electron-nuclear hyperfine interactions; Selection rules and allowed transitions; Frequency-swept and field-swept EPR spectra; First-order perturbation calculations and EPR spectra;How to Analyse First-order EPR Spectra:Recapitulation of the characteristics of first-order EPR spectra; Measuring isotropic hyperfine splitting constants of several free radicals using a ruler and a divider; Identifying the number of equivalent nuclei and their spins; What to do when the outer hyperfine lines are buried in the noise level; Use of computer programs for analysing and simulating first-order EPR spectra;How to Record EPR Spectra:Solid, liquid or gaseous sample; EPR sample tubes; Sample preparation; Degassing and sealing of EPR samples; Choice of solvents; Polar solvents and use of capillary tubes and EPR flat cells; Sample placement inside the microwave cavity; Setting up the EPR spectrometer tuning the microwave frequency, coupling, and AFC; Optimizing the magnetic field position, scan range, modulation amplitude, microwave power, scan time and output filter time-constant, the phase of the microwave bias power and the reference phase of magnetic field modulation frequency;Second-order Effects on EPR Spectra:Why second-order calculations; Spin hamiltonian of hydrogen atom; Separation of unperturbed and perturbation hamiltonians; First-order wavefunctions and energies; Second-order calculation of energies; Transition energies; Fixed- magnetic field and fixed-frequency EPR spectra; Distinction between hyperfine splitting constant and hyperfine coupling constant; Second-order correction for calculating the g-values; EPR spectrum of CF3 radical; Second-order calculations of R-CH2 radical; Second-order effects on the EPR spectrum of a tri-nuclear Co complex;Photochemistry and EPR Spectroscopy:Formation of paramagnetic species by photoexcitation; Means to record EPR spectra of transient radicals; Modifications for in situ photolysis; Need for flowing the reactants; Temperature control; Steady-state EPR spectra under continuous photolysis; Photolysis of p-benzoquinone in alcohol; Photolysis of acetone in 2-propanol;Spin-trapping technique; PBN and DMPO as the trapping agents; Spin-trapping experiment on photolysis of p-benzoquinone in alcohol; Problems with spin-trapping EPR studies; Time-resolved EPR spectroscopy; Recording EPR spectra of transient species by time-resolved EPR technique; EPR spectrum at a given time; Time evolution of EPR signal at a given magnetic field; Photolysis of duroquinone in triethylamine; Photolysis of acetone in 2-propanol;Non-Boltzmann spin distribution and electron spin polarisation.
Electron Spin Polarisation:Example of spin-polarised EPR spectra photolysis of acetone in 2-propanol; Definition of polarisation; The first observation of spin-polarised EPR spectra of H and D atoms; Evidence of electron spin polarisation in steady-state EPR spectra; Comparison of steady-state and time-resolved EPR spectra during the photolysis of p-benzoquinone in 2-propanol; Spin-polarised NMR spectra; CIDEP, CIDNP, CIMP and Electron spin polarisation (ESP); Types of spin-polarised EPR spectra; Mechanism of single-phase hyperfine-independent electron spin polarisation the triplet mechanism (TM); Conditions for TM to operate; Characteristics of EPR spectra arising from TM - Mechanism of mix-phase hyperfine dependent electron spin polarisation; Importance of a pair of radicals and their evolution; Radical pair mechanism (RPM); Overall spin states of the radical pair and interconversion of singlet and triplet radical pairs; Importance of the difference in the frequencies of precession; Conditions for RPM to operate; Characteristics of EPR spectra due to RPM; Dominance of TM or RPM in observed time-resolved EPR spectra; Insight into the detailed dynamics of photophysical and photochemical pathways from spin-polarised time-resolved EPR spectra;Anisotropic Interactions in EPR Spectroscopy:Common examples of anisotropic properties; Averaging of anisotropic properties due to rapid tumbling motions; Need for restricted motion; Origin of g-anisotropy; g-matrix; g2-matrix; Principal axes and principal values of the g-matrix; Effective g-values; Symmetry of crystals; Examples of anisotropic EPR spectra of vacancies in single crystals; EPR lineshapes from powder samples or frozen solutions; Examples of powder EPR spectra; Electron-nuclear dipolar interaction; Anisotropic hyperfine coupling constants; Principal values of the hyperfine coupling constants; Powder patterns due to anisotropic hyperfine coupling; Lineshapes due to combined effects of g-anisotropy and hyperfine anisotropy;Theoretical Basis of isotropic Hyperfine Coupling:Hamiltonian of the isotropic hyperfine interaction; Role of the wavefunction in determining the isotropic hyperfine coupling constant; Concepts of electron density, spin density and spin population; Meaning of negative spin density; Determinantal wavefunction; Atomic spin population; Relation between spin population of C-atom and the hyperfine splitting due to the H-atom in >CH radical; Configuration mixing;Spin Relaxation and Bloch Equations:Magnetisation; Boltzmann distribution of spins at thermal equilibrium; Magnetic susceptibility and Curie law; Non-equilibrium magnetisation and electron spin relaxation process; Blochs proposal of longitudinal (spin-lattice) and transverse (spin-spin) relaxation processes; Time dependence of magnetization in the presence of relaxation Bloch equations - Time dependence of magnetization in the presence of relaxation Bloch equations in the laboratory coordinate system. Rotating coordinates; Time dependence of a vector in a rotating coordinate system; Bloch equations in a rotating coordinate system; Physical meaning; Steady-state solutions of Bloch equations in the rotating coordinate system; EPR lineshapes absorption and dispersion EPR signals; Measuring the relaxation times from the EPR lineshapes, and problems associated with that; Bloch equations as a function of magnetic field
Principles and Applications of Electron Paramagnetic Resonance Spectroscopy by Prof. Ranjan Das, Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai.For more details on NPTEL visit httpnptel.ac.in