EPR line shifts and line shape changes due to spin exchange of nitroxide free radicals in liquids

An expression for the EPR line shape of a nitroxide free radical undergoing spin exchange in the slow exchange limit is derived and tested experimentally and against a rigorous theory. The line shape is the sum of the absorption and dispersion of Lorentzian lines, in which the dispersion component is of opposite signs for the outer lines and zero for the inner. The relative amplitude of the absorption and the dispersion is shown to be a linear function of the spin exchange frequency. Nonlinear least-squares fitting of the spectra allows the separation of the absorption and dispersion components determining their relative amplitudes to high precision yielding values of the spin exchange frequency that are of precision comparable to those derived from the more traditional line broadening. This new way to measure spin exchange frequencies is attractive because there are no complications from dipolar interactions and no measurements at low concentrations are required. The resonance fields of the absorption component of the outer lines shift toward the center of the spectrum as the square of the spin exchange frequency and the observed positions of the lines shift even further due to the absorption-dispersion overlap. The observed shift is also a quadratic function of the spin exchange frequency and involves the unbroadened line width. Both shifts may be used to measure the spin exchange frequency; however, only the observed shift yields values that are of precision comparable with broadening and dispersion-amplitude techniques. The predictions of the theory are tested experimentally using peroxylamine disulfonate in 50 mM K2CO3 at 67 degrees C. At this elevated temperature, the concentration of the radical decreases at a convenient rate making it possible to study a wide concentration range without disturbing the sample. The line broadening was linear with the concentration with a coefficient of correlation r = 0.99996. The spin exchange frequency derived from the amplitude of the dispersion component was within less than 1% of that derived from line broadening and of comparable precision. Spin exchange frequencies derived from the shift of the lines were of lower precision yielding values of the spin exchange frequency about 2% lower than those found from line broadening.