Studies of Heisenberg Spin Exchange in ESR Spectra. I. Linewidth and Saturation Effects

Abstract

A compact general theory for the effect of Heisenberg spin exchange on ESR linewidths and saturation parameters is detailed. The effects of Heisenberg exchange on the linewidths of the tetracyanoethylene anion (TCNE-) radical and the di-tert-butyl nitroxide (DTBN) radical in both dimethoxyethane (DME) and tetrahydrofuran (THF) are investigated. From comparative studies of linewidth as a function of temperature and of radical concentration, TCNE-in DME is shown to undergo strong exchange with a secondorder rate constant of 4.1±0.6X10 9 M-I· sec-I at 15°C. The TCNE-radical in THF exhibits an anomalous concentration-dependent linewidth effect when compared to the theory and to the experiments employing DME as the solvent. The uncharged DTBN radical shows similar spin-exchange properties in both solvents. Possible mechanisms for the anomalous linewidth effect are discussed. The effect of spin exchange on the saturation parameters of the TCNE-radical in DME is investigated in detail, and the experimental results are shown to agree, within experimental error, with the theory developed. Electron-nuclear dipolar and electron-electron dipolar relaxation effects are discussed in terms of their (small) contributions to the experimentally determined relaxation times. Present address:

On spin-exchange and electron-transfer rates in bacterial photosynthesis

“…Eq. 2.16 for Jeff has a certain analogy to a linewidth result in magnetic resonance for a spin hopping (rate constant k) between two sites differing in energy by A (35,37). In the limit of a slow hopping rate (k << A) between two sites there are two distinct resonance lines in an electron spin resonance spectrum.…”

“…[2.9] Similar remarks apply to Os, which equals thereby ks tr (ps-s) Equations for 5c and PD can be obtained by integrating Eqs. 2.6 and 2.7 from t = 0 to t = c. The resulting equations are treated in the Appendix, by using methods (35,36) originally developed in the theory of electron spin resonance line broadening due to Heisenberg spin exchange (35). They are shown in the Appendix to be equivalent to the equation for the -p arising from the solution of the following one-state equation containing effective constants Jeff, kSeff, kTeff, and k2eff: dp --i[Heff,p]-kseffPSpPS-kTeffPTpPT dt k2eff(pTppS + pSppT) [2.10] Here, Heff is given by the sum of HD in Eq.…”

“…A.1 we introduce an ansatz for f-I and determine the coefficients in the result. Namely, we set (35,36) -kD(I-kcR-')PD =-i[HeffD]kSeffPSPDP -kTeffpTp-DpT 4k2eff(pTpDPS + PSPDPT), [A.6] in which I is the identity operator, Heff is an effective Heisenberg spin exchange operator as in Eq. 2.5 with J replaced by Jeff.…”

A paramagnetic molecular voltmeter

“…Dipolar interactions come in the form of field heterogeneity (increasing R 2 alone) and resonant relaxation (assumed to increase R 1 and R 2 equally) and are often assumed to be insignificant for paramagnetic ions in solution (92), but some effects have been reported (46). By selecting fast-relaxing PRAs here, we ensure that collisional spin exchange is strongly favored over dipolar interactions.…”

Electron Spin Relaxation of (Diphenyl) in Dimethoxyethane

“…re is the exchange time which is some times called r2 in literature 9 , ax is the hyperfine coupling constandt in Oe of the ith group of nx equivalent nuclei with spin Ix. This is exactly the same result as that of Currin 10 which can, at least for the central line of the spectrum, easily be extended to low radical concentrations (see Annex).…”