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

Abstract

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 (DD) interactions on 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 HSE and DD have been derived. By employing non-linear 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 if this discrepancy is due to inadequate analysis of the experimental data or an incomplete theory. A key new 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.

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

“…12 The slopes of plots of A B vs c yield the broadening constants 14 B ′ and 15 B ′, which are shown in Figure 2a for the two isotopes; Figure 2b shows their ratios. Data for the open squares in Figure 2a were taken from Part 6.…”

Study of Nanostructural Organization of Ionic Liquids by Electron Paramagnetic Resonance Spectroscopy

“…The HSE and DD induced dispersion can be used for separating the effects of HSE and DD interactions on EPR spectra of nitroxide spin probes in solution. 43 Even in the absence of HSE and DD, which is when the concentration of the spin probe is extremely low, the spectral fitting of the EPR lines still reveals the existence of dispersion in the EPR line shape. This dispersion contribution previously presented in Figure 12 of ref 43 and Figures S2–S4 in the Supporting Information could be explained by the Freed et al approach 44 which is based on the stochastic Liouville equation and involves a relaxation matrix with all contributions: secular, pseudo-secular and non-secular.…”

“…43 Even in the absence of HSE and DD, which is when the concentration of the spin probe is extremely low, the spectral fitting of the EPR lines still reveals the existence of dispersion in the EPR line shape. This dispersion contribution previously presented in Figure 12 of ref 43 and Figures S2–S4 in the Supporting Information could be explained by the Freed et al approach 44 which is based on the stochastic Liouville equation and involves a relaxation matrix with all contributions: secular, pseudo-secular and non-secular. Mladenova et al 26 also suggested that the dispersion signal is of pseudo-secular origin; in other words, from the off-diagonal contributions to the relaxation superoperator.…”

Hydrodynamic and Nonhydrodynamic Contributions to the Bimolecular Collision Rates of Solute Molecules in Supercooled Bulk Water

“…The data analysis leading to the values of d⟨ B ⟩/d c and d B ex /d c has been published previously 25 and is reported in detail in the Supporting Information. The solid line is the SES equation, eq 6, assuming that r ex = r Stokes , setting f eff = 1, and assuming stick BC, Θ = 1.…”

“…Recently, we have been able to separate the two effects 25 by extending the theoretical approach proposed by Salikhov. 21 …”