An ESR Study of Anisotropic Rotational Reorientation and Slow Tumbling in Liquid and Frozen Media

Abstract

A careful study is described of the ESR lineshapes for the peroxylamine disulfonate (PADS) radical dissolved in 85% glycerol solution and in frozen water and D2O. In the frozen media, spectra characteristic of rotational correlation times τR ranging from 1.0 × 10−11sec to > 10−6sec are obtained, while the range in glycerol is from 1 × 10−10sec to >10−6sec. The very rapid rotational motion in frozen water is taken to imply that PADS is rotating in a clathrate cage. The activation energies in ice and 85% glycerol are 14.7 ± 0.1 and 11.3 ± 0.1 kcal/mole, respectively, (from motional-narrowing data). The value for ice is very similar to that obtained for other rate processes in ice. The lineshapes for τR ≲ 10−9sec are analyzed in terms of the familiar spin-relaxation theories valid in the motionally narrowed region. These results are well fitted by the model of axially symmetric rotational diffusion with the symmetry axis in the plane of the N, O, and S atoms and parallel to a line passing through the two S atoms. Diffusion about this axis is found to be 2.9 ± 1 and 4.7 ± 1 times faster for frozen water and glycerol solvent, respectively than about the other axes over a wide range of values of average τR̄. It was possible to obtain these results, because accurate measurements of the g and A tensors for PADS in these media could be made from the well-resolved rigid spectra at X band and 35 GHz; the intrinsic widths in D2O are only about 1.5 G. The spectra in the slow-motional region τ R¯ >10−9sec were simulated utilizing the slow tumbling formulation of Freed, Bruno, and Polnaszek appropriately generalized to include completely asymmetric g and A tensors. The simulated spectra are found, in general, to be in quite good agreement with experimental observations. The agreement is clearly improved by introducing axially symmetric rotational diffusion, as found for the motional-narrowing region, into the simulations. Spectra are simulated for Brownian rotational diffusion as well as for simplified models of free diffusion, which includes inertial effects, and for diffusion by jumps of substantial angle. Improved agreement with experiment is found with some of these latter models. What appears to be a surprisingly small nonsecular linewidth contribution in the motional-narrowing region is briefly discussed in terms of these models.