EPR Line Shifts and Line Shape Changes Due to Spin Exchange Between Nitroxide Free Radicals in Liquids 10. Spin-Exchange Frequencies of the Order of the Nitrogen Hyperfine Interaction: A Hypothesis

Abstract

The behavior of electron paramagnetic resonance spectra due to ¹⁵N and ¹⁴N nitroxide free radicals undergoing spin exchange in liquids at frequencies $\omega_{\text{ex}}$ that are high, of the same order of magnitude as the nitrogen hyperfine coupling constant $A_{0}$, is investigated. The well-known features are reconfirmed: (1) at low values of $\omega_{\text{ex}}$ where the lines broaden, shift toward the center of the spectrum, and change shape due to the introduction of a resonance of the form of a dispersion component; (2) at values of $\omega_{\text{ex}}$ comparable to $A_{0}$, where the lines merge into one; and (3) at values much larger than $A_{0}$, where the merged line narrows. It is found that each line of a spectrum may be decomposed into an admixture of a single absorption and a single dispersion component of Lorentzian shape. These two- or three-line absorption–dispersion admixtures, for ¹⁵N and ¹⁴N, respectively, retain their individual identities even after the spectrum has merged and has begun to narrow. For both isotopes, the average broadening and integrated intensities are equal to the predictions of perturbation theory although, in the case of ¹⁴N, the outer lines broaden faster than the central line and intensity moves from the outer lines to the central line. In fact, the outer line intensity becomes zero and then negative at higher values of $\omega_{\text{ex}}$ which is compensated by the central line becoming more intense than the overall integrated intensity. For both isotopes, the dispersion components and the line shifts depart from the perturbation predictions. The results are presented in terms of measurable quantities normalized to $A_{0}$ so that they may be applied to any two- or three-line spectrum.