Director fluctuations and ESR spectra: a slow-motional treatment

The analysis of the influence of director fluctuations on the ESR spectra of a spin probe dissolved in oriented phases (liquid crystals, membranes) requires a slow-motional treatment because the director field has always slowly relaxing components. Therefore, under the assumption of fast molecular tumbling of the spin-probe, the stochastic Liouville equation has to be solved for the coupling between the spin degrees of freedom and the fluctuating director field. The condition of small amplitude of director fluctuations is invoked to derive explicit solutions for the line widths in the presence of hyperfine interactions, with distinct contributions from the secular and the pseudosecular terms of the spin Hamiltonian. A perturbational treatment with respect to the nuclear spin states allows one to quantify the pseudosecular contributions, while the secular ones are exactly accounted by employing the methodology developed for the analogous analysis of nuclear spin relaxation due to quadrupolar interactions [Frezzato, D.; Kothe, G.; Moro G. J. J. Phys. Chem. B 2001, 105, 1281]. Model calculations are reported for a nitroxide spin probe (PD-tempone) in a nematic phase to assess the role of the secular and pseudosecular contributions and to characterize the dependence of the line shapes on the relevant physical parameters. The relative incidence of tumbling dynamics and director fluctuations on the line widths is also investigated.