EPR Line Shifts and Line Shape Changes Due to Heisenberg Spin Exchange and Dipole–Dipole Interactions of Nitroxide Free Radicals in Liquids: 9. An Alternative Method to Separate the Effects of the Two Interactions Employing 15N and 14N

A method to separate the effects of Heisenberg spin exchange (HSE) and dipole−dipole (DD) interactions on EPR spectra of nitroxide spin probes in solution by employing N and N nitroxide spin probes in parallel experiments is developed theoretically and tested experimentally. Comprehensive EPR measurements are reported of 4-oxo-2,2,6,6tetramethylpiperidine-d16;1N-1-oxyl (perdeuterated N Tempone; 15pDT), in 70 wt % aqueous glycerol as functions of concentration and temperature. The method, termed the relative broadening constant method (RBCM), is demonstrated by using the present results together with those in the literature that employed perdeuterated N Tempone (14pDT) under identical conditions. In principle, the separation of DD and HSE is dependent on the model of diffusion and molecular-kinetic parameters; however, within present day experimental uncertainties, the RBCM method turns out to be insensitive to the model. The earlier methods to separate DD and HSE by measuring the dispersion component introduced by the two interactions shows general agreement with the RBCM; however, there are discrepancies larger than estimated uncertainties due to random errors. Thus, further support is found for Salikhov’s recent theory of the effects of DD and HSE on EPR spectra (Appl. Magn. Reson. 2010, 38, 237); however, detailed confirmation is still lacking. The RBCM affords a possible approach to separate HSE and DD in spectra complicated by slow motion and/or overlap with other resonance lines, allowing the method to be used in situations more complicated than low-viscosity simple liquids. ■ INTRODUCTION Thiswork adds onemore tool to separate the effects of dipole−dipole interactions (DD) and Heisenberg spin exchange (HSE) on EPR spectra of dilute solutions of nitroxide free radicals (nitroxides) in low-viscosity liquids. Frequently used abbreviations and acronyms are listed in Table 1. We briefly summarize the progress to date in earlier papers in this series and refer the reader to those papers for detailed discussion. Part 1 demonstrated that HSE introduces a dispersion component into the spectrum from which the rate constant of HSE, KHSE, may be deduced with a precision rivaling that of line broadening. In addition, Part 1 showed that line shifts could also be used to estimateKHSE. In Part 1, 1 Fremy’s salt was measured in water at 343 K where undoubtedly DD contributed negligibly to the spectrum. Parts 2, 3, and 4 continued investigations in solvents of low viscosity and at high temperatures in order to avoidDDand dealt with large values of KHSE, inhomogeneous broadening, and five lines rather than the usual three. In Part 2, the line shifts were foundnot to conform with early theoretical predictions; thus, they could not be used to deduce KHSE. We incorrectly speculated that the discrepancy was due to inhomogeneous broadening,Binhom, caused by unresolved proton or deuteron hyperfine interactions and magnetic field modulation. Part 3 advanced a more plausible proposal, attributing the line-shift discrepancy to HSE due to re-encounters of the same pair while residing in a cage as proposed by Salikhov. Part 4 presented further evidence that Salikhov’s re-encounter mechanism was correct, and Part 5 exploited the mechanism to study reencounter collisions in a series of alkanes. Finally, in Part 6, we purposely studied a viscous liquid, 70 wt % glycerol in water (70%AG), in order to address the separation of DD and HSE. Received: May 30, 2014 Revised: July 16, 2014 Published: July 18, 2014 Table 1. Abbreviations and Acronyms DD dipole−dipole interactions HSE Heisenberg spin exchange nitroxides nitroxide free radicals SE Stokes−Einstein equation instrumental dispersion in phase magnetization, commonly due to an improperly balanced microwave bridge Binhom inhomogeneous broadening caused by unresolved proton or deuteron hyperfine interactions and magnetic field modulation FIT or FITTING linear or nonlinear least-squares fit, noun or verb 70%AG 70 wt % glycerol in water HVL high-viscosity limit to evaluate DD contributions LVL low-viscosity limit to evaluate DD contributions Article