Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water

Abstract

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting for finding the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14N- and 15N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Measuring radical diffusion in viscous liquids by electron paramagnetic resonance

“…However, both fitting methods give the same results after suitable transformations of the EPR parameters obtained by the latter method [19]. The HSE-DD separation method is further improved by iterative solving of the kinetic equations for the spin evolution of two radicals moving according to the continuous diffusion model and interacting by HSE and DD interactions [19]. The obtained relations for the concentration coefficients of spin dephasing, spin coherence transfer, and hyperfine splitting were then used to calculate the diffusivities of radicals.…”

“…2a-b). The original spectral function for the absorption EPR spectra of 15 N-and 14 N-labeled radicals interacting by HSE and DD interactions was obtained from the modified Bloch equations [7,19]. It has the form:…”

“…We applied the formalism of the kinetic equations for the spin density matrices of radical pairs [6,16,21] for the system of radicals described in the previous section. The concentration coefficients in G/M units were found to have the following form for the 15 N-pDTEMPONE solution [19]:…”

“…[7]. The absorption-dispersion function fitting and HSE-DD separation method were improved in a follow-up EPR study of 14 N-pDTEMPONE and 15 N-labeled pDTEMPONE ( 15 N-pDTEMPONE) diffusion in water [19]. The EPR spectra of both radicals were fitted to the original spectral function derived from the modified Bloch equations in the presence of HSE and DD interactions.…”

“…The original function fitting method provides the original EPR parameters directly from the Bloch equations, unlike the absorption-dispersion function fitting method [14,15]. However, both fitting methods give the same results after suitable transformations of the EPR parameters obtained by the latter method [19]. The HSE-DD separation method is further improved by iterative solving of the kinetic equations for the spin evolution of two radicals moving according to the continuous diffusion model and interacting by HSE and DD interactions [19].…”