Studies of heisenberg spin exchange in ESR spectra. I.Linewidth and saturation effects

A compact general theory for the effect of heisenberg spin exchange on ESR linewidths and saturation parameters is detailed. The effects of heisenberg exchange on the linewidths of the tetracyanoethylene anion (TCNE<SUP>-</SUP>) radical and the di-tert-butyl nitroxide (DTBN) radical in both dimethoxyethane (DME) and tetrahydrofuran (THF) are investigated. From comparative studies of linewidth as a function of temperature and of radical concentration, TCNE<SUP>-</SUP> in DME is shown to undergo strong exchange with a second-order rate constant of 4.1&#177; 0.6 &#215; 10<SUP>9</SUP>M<SUP>-1</SUP>. sec<SUP>-1</SUP> at 15&#176;C. The TCNE<SUP>-</SUP> radical in THF exhibits an anomalous concentration-dependent linewidth effect when compared to the theory and to the experiments employing DME as the solvent. The uncharged DTBN radical shows similar spin-exchange properties in both solvents. Possible mechanisms for the anomalous linewidth effect are discussed. The effect of spin exchange on the saturation parameters of the TCNE<SUP>-</SUP> radical in DME is investigated in detail, and the experimental results are shown to agree, within experimental error, with the theory developed. Electron-nuclear dipolar and electron-electron dipolar relaxation effects are discussed in terms of their (small) contributions to the experimentally determined relaxation times