ESR line shapes in the slow-motional region: Anisotropic liquids

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Abstract
It is shown how the analysis of Freed et al. for ESR lineshapes in the slow tumbling region may be generalized to include anisotropic liquids. Particular emphasis is given to the case of nitroxide radicals in liquid crystal environments with cylindrically symmetric restoring potentials U (β). It is found that when |U(β)|≲ kT , spectral appearances are qualitatively (but not quantitatively) similar to those for isotropic liquids. In particular, the spectra are sensitive to the model of reorientation. They are also predicted to be a very sensitive indicator of effects of anisotropicviscosity. The analysis given for the motional narrowing region yields analytic expressions for the needed spectral densities, where previously only numerical results had been obtained. The analytic expressions are valid when |U(β)|≲ kT . Analytic solutions to the rotational diffusion equation appropriate for |U(β)|≫kT are given and it is outlined how they may be applied to magnetic resonance.

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