1. Introduction ................................................ 1 2. Theory of Spin Exchange .................................... 11 2.1 Exchange Interaction Between Two Paramagnetic Particles 11 Dependence of Interaction Energy on Spin ................ 11 Spin-Hamiltonian of Exchange Interaction ................ 13 The Nature of Exchange Interaction. The Two-Electron System ................................. 13 Interaction Between Many-Electron Systems. Delocalization and Spin Polarization .................... 16 Anisotropy of Exchange Interaction ...................... 19 Semiempirical Estimates of Exchange Integral ............ 20 2.2 Qualitative Description of Spin Exchange Process ........ 25 Spin Exchange ........................................... 25 Spin Exchange in a Two-Electron System .................. 26 Spin Density Matrix ..................................... 28 Spin Motion Due to Exchange Interaction ................. 30 2.3 Formal Kinetics of Spin Exchange in Magnetically Dilute Solutions ........................................ 34 Binary Collision Approximation .......................... 34 Rate of Bimolecular Spin Exchange Process ............... 35 Kinetics of Spin Exchange for Particles with Spins S=1/2 36 Kinetic Equations for Free Radicals Showing Hyperfine Structure (HFS) in Their ESR Spectra .................... 40 2.4 Spectroscopic Manifestations of Spin Exchange ........... 41 Spectral Diffusion Due to Spin Exchange ................. 41 Shape of ESR Spectra .................................... 42 Slow Exchange ........................................... 45 Fast Exchange ........................................... 48 Other Methods of Measuring the Rate of Spin Exchange .... 49 Effect of Saturation .................................... 50 Electron-Electron Double Resonance (ELDOR) .............. 53 Electron Spin Echo ...................................... 55 2.5 Theory of Sudden Collisions ............................. 56 2.5.1 Model of Sudden Collisions ........................ 56 Basic Assumptions ................................. 56 Equations for the Estimation of τc ................ 58 2.5.2 Kinetic Equations ................................. 61 Steady-State Equation for the Operator of Collision Efficiency .............................. 64 2.5.3 Spin Exchange Between Radicals .................... 65 Model System ...................................... 65 Spin Exchange Between Radicals in the Presence of Hyperfine Interaction .......................... 70 2.5.4 Spin Exchange Between Radicals with Anisotropic Interaction ....................................... 70 Rotation of Partners at the Moment of Their Contact ..................................... 71 Orientational Relaxation of Particles in Intervals Between Reencounters .................... 78 2.5.5 Spin Exchange of Radicals with Other Paramagnetic Particles ............................ 82 Spin Exchange Between Radicals and Spins SB with Long Times of Paramagnetic Relaxation ............. 83 Shape of ESR Spectra .............................. 85 The Influence of the Relaxation of Spin SB on the Rate of Exchange .............................. 87 Anisotropy of Spin Exchange ....................... 90 2.5.6 Spin Exchange in Biradicals ....................... 91 The Model ......................................... 92 Kinetic Equations ................................. 93 The ESR Spectrum of Nitroxide Biradicals .......... 94 2.6 The Model of Diffusive Passage .......................... 96 The Model ............................................... 97 An Equation for the Operator of Collision Efficiency .... 98 The Kinetic Equations ................................... 99 The Spin Exchange Between Two Kinds of Particles with Spins SA = SB = 1/2 ...................................... 99 Comparison of Results Obtained from Models of Sudden Collisions and Those of Diffusive Passage .............. 103 3. Experimental Measurement of Spin Exchange Rate ............ 107 3.1 Experimental Measurement of Spin Exchange Rate Constants from ESR Spectra .......................... 107 3.1.1 Exchange Between Identical Particles with S = 1/2 .................................. 107 Doublet Spectrum with a Zero Initial Width .... 107 Complex Spectra ............................... 110 Determination of Rate Constants from Exchange Broadening of Complex Spectra ................. 111 Determination of Rate Constants from Exchange Shift of the Lines of Complex Spectra ......... 116 Determination of Rate Constants from Exchange Narrowing of Complex Spectra .................. 117 Peculiarities of Exchange Narrowing in Concentrated Solutions ........................ 118 Comparison of Spin Exchange Rate Constants Measured by Different Techniques .............. 119 3.1.2 Exchange Between Different Particles .......... 120 3.2 Other Methods of Measuring the Spin Exchange Rate Constants ........................................... 127 3.2.1 Continuous Wave Saturation Method ............. 127 3.2.2 Electron-Electron Double Resonance ............ 130 3.2.3 Electron Spin Echo ............................ 132 3.3 Separation of Exchange and Dipole-Dipole Contributions to Concentration Broadening of ESR Lines ............................................... 133 Theoretical Estimation of Dipole Broadening ......... 134 Experimental Estimation of Dipole-Dipole Contribution at Low Viscosity ....................... 137 Separation of the Cases of Exchange and Dipole - Dipole Broadening According to Viscosity and Temperature Dependences ............................. 139 3.4 Separation of the Cases of Weak and Strong Exchange 142 4. Spin Exchange in Chemistry and Biology .................... 147 4.1 Study of Diffusion Collisions in Solutions .......... 148 Hydrodynamic Model of Diffusion Collisions .......... 148 Potentialities of Spin Exchange ..................... 149 4.1.1 Collisions in Single-Component Solvents ....... 152 Spin Exchange Between Radicals ................ 152 Spin Exchange Between Free Radicals and Paramagnetic Complexes ........................ 158 4.1.2 Collisions in Complex Systems ................. 165 Binary Solvents ............................... 166 Liquids Near Critical Points .................. 168 Polymeric and Heterogeneous Systems ........... 171 Collisions of Macroradicals ................... 173 4.1.3 Study of Intramolecular Collisions of Paramagnetic Fragments ........................ 175 4.2 Estimation of the Energy of Exchange Interaction During Collisions ................................... 178 4.2.1 Free Radicals ................................. 180 4.2.2 Spin Exchange with Metal Complexes ............ 182 4.2.3 Discussion of Results ......................... 187 4.3 Collisions of Charged Particles ..................... 192 4.3.1 Experimental Results .......................... 193 Spin Exchange in Solutions of Anion Radical (SO3)2NO2- ..................................... 193 Spin Exchange Involving Charged Nitroxide Radicals ...................................... 198 Spin Exchange Between Anion Radicals in Organic Solvents .............................. 203 4.3.2 Comparison of Experiments on Spin Exchange with the Diffusion Theory of Collisions of Charged Particles in Liquid ................ 204 4.3.3 Study of Collisions Between Aquo Complexes of Transition Metals .......................... 207 Role of Counterions in Collisions of Aquo Complexes of Vanadyl .......................... 207 An Example of the Process with Weak Influence of Electrostatic Repulsion .................... 211 4.4 Biological Applications of Spin Exchange ............ 213 Paramagnetics Used as Spin Probes ................... 214 4.4.1 Measurement of Binary Collision Rate of Molecules in Biological Systems ............... 214 4.4.2 Study of Location of Paramagnetic Centers in Bio-polymers ............................... 217 Quantitative Interpretation of the Values of Ke for Spin Exchange Processes Involving Paramagnetic Centers of Biopolymers 220 4.4.3 "Development" of Individual ESR Spectra of Spin Labels via Spin Exchange .............. 222 4.4.4 Spin Exchange Titration ....................... 225 Kinetics of Reactions Involving Oxygen Molecules ..................................... 225 Coordination of Paramagnetic Ions by Macromolecules ................................ 226 4.4.5 Other Applications ............................ 227 4.5 Conclusion .......................................... 228 List of Frequently Used Notations and Abbreviations ......... 231 References .................................................. 233 Subject Index ............................................... 241