Electron Paramagnetic Resonance Line Shifts and Line Shape Changes Due to Heisenberg Spin Exchange and Dipole-Dipole Interactions of Nitroxide Free Radicals in Liquids 8. Further Experimental and Theoretical Efforts to Separate the Effects of the Two Interactions

The work in part 6 of this series (J. Phys. Chem. A 2009, 113, 4930), addressing the task of separating the effects of Heisenberg spin exchange (HSE) and dipole-dipole interactions (DD) on electron paramagnetic resonance (EPR) spectra of nitroxide spin probes in solution, is extended experimentally and theoretically. Comprehensive measurements of perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (pDT) in squalane, a viscous alkane, paying special attention to lower temperatures and lower concentrations, were carried out in an attempt to focus on DD, the lesser understood of the two interactions. Theoretically, the analysis has been extended to include the recent comprehensive treatment by Salikhov (Appl. Magn. Reson. 2010, 38, 237). In dilute solutions, both interactions (1) introduce a dispersion component, (2) broaden the lines, and (3) shift the lines. DD introduces a dispersion component proportional to the concentration and of opposite sign to that of HSE. Equations relating the EPR spectral parameters to the rate constants due to HSE and DD have been derived. By employing nonlinear least-squares fitting of theoretical spectra to a simple analytical function and the proposed equations, the contributions of the two interactions to items 1-3 may be quantified and compared with the same parameters obtained by fitting experimental spectra. This comparison supports the theory in its broad predictions; however, at low temperatures, the DD contribution to the experimental dispersion amplitude does not increase linearly with concentration. We are unable to deduce whether this discrepancy is due to inadequate analysis of the experimental data or an incomplete theory. A new key aspect of the more comprehensive theory is that there is enough information in the experimental spectra to find items 1-3 due to both interactions; however, in principle, appeal must be made to a model of molecular diffusion to separate the two. The permanent diffusion model is used to illustrate the separation in this work. In practice, because the effects of DD are dominated by HSE, negligible error is incurred by using the model-independent extreme DD limit of the spectral density functions, which means that DD and HSE may be separated without appealing to a particular model.