Electron spin-echo envelope decays and molecular motion: Rotational and translational diffusion

Abstract

A description is given of the two-pulse electron spin-echo envelope behavior for dilute solutions of free radicals over a temperature range where the radical and matrix molecules are undergoing increased molecular tumbling. As the temperature is increased from 77 K, the phase memory time for the anthracene-d10 radical anion in 2-methyltetrahydrofuran (MTHF) first decreases, goes through a minimum between 104 and 140 K, increases to a maximum value at 180 K, and then decreases again up to 300 K. The temperature dependence of the phase memory time for the neutral radical 2,2,6,6-tetramethyl-4-hydroxypiperidine-1-oxyl in MTHF is essentially the same. For peroxylamine disulfonate (PADS) in the glycerol-water and water matrix, only a minimum value is observed, since on the high temperature side of this minimum, the free induction decay signal is much larger than the echo. The low temperature side of these minima defines the slow tumbling region, i.e., τ ≪τc, where τc is the correlation time for the motion and τ is the interpulse time, whereas on the high temperature side τ≫τc. In the former region, the molecular tumblings render anisotropic interactions time dependent and produce additional local field fluctuations which account for the decrease of the phase memory time with increasing temperature. In the latter region the local field fluctuations are so fast that they average out the local fields and effect an increase in phase memory time with increasing temperature. Hence, the occurence of the minimum is analogous to a motional narrowing phenomenon. Expressions for the phase memory time and the shape of the echo envelope decay are derived assuming a Gauss-Markoff model for the rotational and translational diffusion effects. The predicted general behavior of the phase memory time is in agreement with observations in that a minimum value is predicted. Estimates of the minimum value of the phase memory time for the PADS radical in a glycerol-water matrix (85:15 wt%) indicate that at temperatures close to the minimum the phase memory time is probably determined by the local field fluctuations arising from a modulation of the nitrogen anisotropic hyperfine interaction by the radical rotational motions, whereas matrix hyperfine interactions and rotational and translational diffusion of the matrix molecules play only a minor role. The temperature dependence of the amplitude modulation in the echo envelope for the anthracene-d10 radical anion in MTHF is tentatively interpreted to mean that either the modulation pattern is less sensitive to radical rotations than is the phase memory time or, alternatively, the correlation time for matrix rotations is less than that for radical rotations. The decrease of the phase memory time at temperatures above the maximum value is due to Heisenberg spin exchange which is a result of radical-radical encounters brought about by increased radical translational diffusion.