The influence of director fluctuations on molecular reorientation of a small probe molecule in a liquid-crystalline environment

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Abstract
The influence of director fluctuations on a probe molecule dissolved in a nematic liquid crystal is calculated to all orders using the gaussian properties of the director field. Consequences for the N.M.R. spectrum and relaxation through quadrupolar interaction of the probe molecule are indicated. It is found that the equilibrium distribution of molecular orientations, and consequently quadrupolar spectral splittings are virtually unchanged by fluctuations in the director field. The spectral densities are also obtained and it is shown that in addition to J 01 also J 00 and J 02 become frequency dependent in the N.M.R. frequency range. The frequency dependence of J 00 and J 02 has a logarithmic contribution; the magnitude of the frequency dependent contribution to J 02 is, however, insufficient to explain experimental results.